Infants learn how to socialize and express their emotions by interacting with adults, primarily with their parents. Developing a positive, "happy" bond with the mother is good for babies, and depression interferes with that.
Maternal postpartum depression during the child’s first year of life
significantly predicted internalizing behavior problems. This
association was not found if maternal depression occurred before
pregnancy or during the prenatal period. 
Positive communication styles and maternal warmth observed in
mother-child interactions have been associated with prosocial behavior
and positive self-concept development in children (Kochanska,
Children of depressed mothers don't get the same amount of positive interaction and smiling faces, and that impacts their ability to interact with other people, feeling attached to parents, and other social development. This isn't (necessarily) just short-term.
Results indicated that ... degree of maternal depression ... had
independent predictive associations with youths' externalizing
symptoms and functional impairment. 
(I can't access the full text of this article, so have quoted the abstract.)
It's more complicated than simply "whether the mother is depressed" — paternal depression, attention, and behavior play a role in either exacerbating or ameliorating the effects. If a father is smiling, playing, and taking care of the infant, then there's still some positive interaction.
These findings point to the presence of psychopathology in fathers as
a risk factor for toddlers’ externalizing behavior problems when
mothers have been previously depressed, and for toddlers internalizing
problems when mothers have either a history of or current depressive
symptoms... Paternal psychopathology may increase the likelihood of
behavior problems in at-risk toddlers directly, as depressed and/or
anxious fathers may provide inconsistent and permissive parenting, or
indirectly, if they are less involved with caring for their children
and leave depressed mothers sole responsibility for the daily
behavioral management of toddlers. 
One of the key things that all the articles mention is that their research reinforces the importance of intervention, to treat maternal depression and thereby alleviate the problem for the child.
Speaking personally: as somebody who went through post-partum depression twice, I suggest you be careful in how you introduce the influence of maternal depression, if you even bring it up at all. Depression isn't something that you can just snap out of, and being told your sadness is hurting our baby! would have just sent me further into depressive spirals, helping neither me nor my child (nor, ultimately, my partner). It may be more productive to focus on encouraging her to seek help for her own sake, while you personally focus on being a positive parent and partner. That's something you can do whether or not she gets treatment for her depression.
Whether he will grow to dislike you -- I assume you are wondering whether he blame you for his mother being sad. My thoughts on this are less evidence-based. His feelings towards you will be pretty dependent on how you're interacting with your partner and your son during her crying episodes. (And, as the research above seems to indicate, his emotional well-being will be influenced, not just whether he likes you.) Seeking compromise, avoiding language or situations you know will be triggers, keeping a hold on your frustration and temper — not necessarily giving in on everything to avoid conflict, but working around the restrictions and obstacles that her disease is establishing. Couples counseling may be useful both to help you interact positively with each other, and also to give her a place to begin getting help and treatment for her depression.
Bagner, D. M., Pettit, J. W., Lewinsohn, P. M., & Seeley, J. R. (2010). Effect of Maternal Depression on Child Behavior: A Sensitive Period? Journal of the American Academy of Child and Adolescent Psychiatry, 49(7), 699–707. DOI
Dietz, L. J., Jennings, K. D., Kelley, S. A., & Marshal, M. (2009). Maternal Depression, Paternal Psychopathology, and Toddlers’ Behavior Problems. Journal of Clinical Child and Adolescent Psychology, 38(1), 48–61. DOI
Nelson, Denise R.; Hammen, Constance; Brennan, Patricia A.; Ullman, Jodie B. The impact of maternal depression on adolescent adjustment: The role of expressed emotion. Journal of Consulting and Clinical Psychology, Vol 71(5), Oct 2003, 935-944. DOI