In Long Way From Home it is revealed that Svetlana is pregnant with what is supposedly Mickey's child, and that he is going to marry her after Terry Milkovich hires her to rape Mickey after he catches him and Ian together in Cascading Failures.
In The Legend of Bonnie & Carl, Svetlana is angry that Mickey doesn't seem to even care about Yevgeny and also insists that she needs money for baby supplies.
In Emily, Svetlana has insisted upon a Russian Orthodox baptism for Yevgeny.
In Lazarus, Svetlana insists again that Mickey take a more active role in helping with the baby.
In season five, it seems that Mickey is more involved, albeit reluctantly, in Yevgeny's life, though Ian enthusiastically helps take care of him. In Crazy Love, Ian steals Yevgeny and takes him on a road trip in a full psychotic break which also shows Mickey's concern for his son's safety.