I want to feel closer to him.

I am 35/f and my boyfriend is 33/m. We have been together for 1.5 years and live together. I feel like he isn't making much effort into the emotional aspect of our relationship. He has depression and anxiety so I try to factor that in. When he is upset he doesn't tell me what's on his mind. He says he doesn't want to burden me with his thoughts. I've explained to him that I don't feel close to him. I even tried playing "We are not really strangers". It was nice because I enjoyed him sharing his thoughts for once. But I want to know him more on a deeper level. I want him to feel like he can come to me for advice and an ear to listen to. He sleeps a lot which is alot to do with his depression so when he is awake I try to spend time with him. Sometimes I'm at a loss and settle for just being in the same room as him. How can I get my boyfriend to open up more?