Several studies and papers have been written about doctors and divorce. It turns out my memory of the numbers wasn't exactly correct, but it is more optimistic than many have said:
United States population overall: 40%
Physicians overall: 32%
Psychiatrists: 51%
Surgeons: 33%
Pediatrics, IM: 23%
Physicians married to another physician: 11%
Female physicians 37%, males 28%
That data is from Rollman BL et al, "Medical specialty and the incidence of divorce." There are others as well. JAMA has a more recent article that found no evidence that physicians are more divorce-prone than the general populace. If you trust the above data, surgeons are more stable than the general populace.
At my institution, 80% of the NS attendings are married. One is a very devoted father, and frequently attends his kids' school and sports events. Like I said, it is what you make of it. It might cost you some time in your research lab, or even some time in the OR, but IMO there is no field of medicine where it's impossible to build a stable, successful family. You just have to make it a priority.