"We just started talking about stuff -- 'Do you have kids?' and I was like, 'I have three,' and he said, 'I have three,'" Dempster said. "He said, 'Our daughter has some special needs,' and stuff. They're both chromosome and genetic disorders -- it's crazy."
Dempster, 35, one of the Cubs' starters, has crusaded to raise awareness nationally for 22q11.2 deletion (DiGeorge syndrome), something his daughter Riley is battling. She turns 3 on April 1.
Miller, 39, is a non-roster invitee, hoping to find a spot in the bullpen with his 10th team. This spring, he's also checking his phone regularly for news from his Florida home about his daughter, Grace, who has a genetic defect to the 16th and 20th chromosomes. The disorder is so rare, there's no name for it. Grace can't walk or talk and needs a tracheal tube to breathe.
She's the only child in the U.S. to ever live beyond a year's age with the condition. She'll celebrate her eighth birthday in June.
"My first day down here, I came in and wanted to work out, and I said, 'I'll throw with you to break up the jet lag,'" Miller said of his first meeting with Dempster at Fitch Park.
That introductory conversation evolved to their children.
"[His daughter] has the trach out, which is a huge step -- thank you, Jesus, for that," Miller said of Riley. "We're praying our daughter can eventually get to that point. She's come close and then she takes a few steps back. Eventually she'll get there, that's our belief."
For the first 18 months of Riley Dempster's life, she could not be submerged in water because of the trach. Now, she spends three to four hours swimming in the pool. She's going to preschool a couple days a week.
"A lot of kids with 22q struggle with math and she's counting to 10 on her fingers," Dempster said. "She's ahead of the game because of the early detection."
For the Millers, it's a daily struggle. Trever's wife, Pari, showed her strength during the 2008 American League Championship Series. While Trever and the Rays were celebrating the win at Tropicana Field, Grace was in the stands, choking on her own mucus. She nearly died. Pari performed a trachea change to clear Grace's airway.
"People probably know Grace more than they know me," Miller said Wednesday of his daughter, who had to spend a lot of time in the hospital. "She's doing well. Last year was a rough year. She was very sick. My wife didn't get to come out nearly as often to see me, which means the kids didn't get to see me as often.
"This year, so far, knock on wood, praise God, she's doing a lot better," he said. "She's got a kidney stone thing we've been dealing with the past three, four years. She's a trooper. She's the toughest thing I've ever seen. I call her 'Nails.' She's tough as nails.
"We're doing the Gracie dance, just trying to keep her stable and thriving and living life with us," Miller said. "We love her."
While Riley's disorder is unique, Grace's is even more unusual.
"The cases they gave us were from the 1980s and medicine has come so far since then," Miller said. "There were only a handful of those, 15 to 20 cases over the past 20 years. The doctors didn't know what to tell us. Those kids never lived a year. It wasn't good, it was a grim outlook. Grace surprised and shocked the world, and through God, he's shown us there are true miracles."
Miller knows something about endurance. He's competed in three marathons and two triathlons, and is a huge fan of 5K races. Every November, he runs a race near his Land O'Lakes, Fla., home, pushing Grace in a racing stroller.
"I got into running about seven years ago and it's made a great difference in my stamina throughout the season, and it keeps me fit and in shape to keep up with the youngsters around here if not push them a little bit to motivate them to get a little better," he said.
He has a few gray hairs but doesn't feel old, even though someone on the Cubs mentioned that Miller was a teammate of his uncle's.
Since 1996, Miller has played for the Tigers, Astros, Phillies, Dodgers, Blue Jays, Rays, Cardinals and the Red Sox. Last year, he posted a 3.80 ERA in 48 games for three teams, the Cardinals, Blue Jays and Red Sox. This year, the Cubs are looking for one other lefty in the bullpen to possibly complement James Russell. Miller's experience could help him.
"I didn't get a whole lot of offers," he said of the offseason. "My perception of the game changed a little last year. I have to work on that this year. I have to re-establish myself as the quality pitcher that I know I've been throughout my career and even more.
"I want to be a little bit better than people who have known me throughout my career to stay in this game because that's what I want to do," he said. "I want to pitch and play as long as I possibly can, and not only for me but for my kids and my wife and my little girl. Gracie is my inspiration.
"I'm never going to quit," he said. "The game will be done with Trever and I'll move on. There will be no retirement party, no riding into the sunset for this old left-hander, that's not going to happen."
When his career is over, Miller plans on competing in more triathlons. His family has taken up running -- his wife has run more half marathons than he has, and hopes to run a full marathon this year. His other two children, 15-year-old Tyler and 13-year-old McKenzie, have joined cross country teams.
"It's given us quality time together," he said.
Quality time is what every dad wants with their children. Just ask Dempster and Miller.
"I wish [we connected] under different circumstances," Dempster said, "but at the same time, at least it shows you that you're not alone."
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter@CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.