If a mom has bipolar disorder and a dad has depression, what are the chances the child will have either problem when he grows up?

Hard to say: The genetic component increases the child's chances. But, the environment, and personality also play a very large role.

Depression: With any major mental disorder, having a first degree relative who is afflicted increases the likelihood that children may have some form of the disease, although it certainly is not inevitable.

The stats: From the literature: 35% chance if one parent has it. 75% if both parents have it. These are the probabilities. Literature says depression & anxiety push the odds slightly more. Keep in mind that a more stressful environment will play a major role in pushing these probabilities forward. A more stable environment is always protective against gene expression of any genetic vulnerability. take care