This is going to sound like I'm completely ignoring your question, but bear with me.
You mention he pays the phone bill because you stay home with the baby. Does that mean you never go out?
You mention you've been feeling down lately. Do you have friends? Maybe a Mum's group? A life outside your SO and child?
Now you're wondering, what does any of this have to do with why my SO feeling down?
A lot, potentially.
I know that when my husband is down in the dumps, I feel like it's all on me to cheer him up. Most of the time, the reason he's feeling down has nothing to do with me, so there's nothing I can do to cheer him up. In your case, if your SO feels like he has to keep your mood up, to be the optimist in the family, that could get burdensome.
So although it sounds unrelated, my suggestion for cheering up your SO is to join a Mum's group, make some friends, and find ways to cheer yourself up outside of your relationship with him. I'm not saying it's your fault, not by a long shot. But it's amazing how much your partner's mood can affect your own. So while it's not your fault that he's feeling down, maybe making an effort to be the optimist for a while can help pull him out.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker