I would tell your husband:
It is ok and fine to feel this way, and fully valid. Many parents feel depressed, and it is real and ok.
But
2 things:
1, being a parent is never about making you happy. Treat it like a job - you have to do it, regardless of whether it makes you happy. Your happiness is second now to your responsibilities to your child's wellbeing.
That is harsh, but I've seen people who start by thinking "I'm depressed because of parenting" and then their solution is to run-away from it. Give it all to their partner, or worse ruin the relationship. Because fundamentally they still put their happiness over their child's wellbeing. That option needs to be taken away.
But then number 2, give him hope.
tell him that for most dads, parenting gets a lot better at around 3.5-5 years old. All of a sudden the child is old enough to join in with things that the dad likes.. they can actually play together properly, play football, go on hikes, play games, share interests etc. This is normally when dads get more into parenting (if they are good dads). Yes it is tough now, but he can lay the groundwork for this now. Start getting his child into football, take them for short hill walks.. lay that ground work.
An example from my son is that we go to the UK each summer, and I love hiking on dartmoor. I took my son for the first time at 2.5, and we just did a bit. We climbed (with carrying) through one short route... But that laid down a happy memory for him, and then at 3.5 we did more. And then at 4.5 we went back and did a pretty long hike with an over-night camping. Now at 5.5 this summer, he cant wait to go back to have another adventure.
It wasn't fun at 2.5, but it laid down the groundwork for a relationship and experience that is now fun, a few years later.
Overall, though he needs to take responsibility and start problem solving. Look at each part and with you, find a solution that could help improve things ,and keep iterating and changing until it does. But (big but) those improvements have to be with the best interest of your child and you as well, and cannot be "well I need to go do my stuff and ignore you both, because that will keep me happy" as quite a few dads do...