Definitely requires some pushiness to deal with someone fighting severe depression (I have issues with this).
They can't (as book said) make themselves do it.
The secrecy could be a life/death issue.
She needs help. She won't get it for herself. So he needs to put his foot down and REQUIRE it. If that means he supplements-so be it. If that means that he drives her to the doctor/counselor himself-so be it.
If you can reassure her that this is a MEDICAL issue-not a sign of her being a bad/good mom and that you want to HELP her through it-that would be good. No idea if you can convince her-but keep saying it. Because she IS NOT thinking coherently if she is struggling with depression. She may not realize it-but it's the truth. The more she hears it-the more likely she'll grasp it LATER.
Don't forget to take a break too. He and you need breaks-so you need to find others who can help. The people supporting someone with severe depression are at higher risk of getting depressed too. It's EXHAUSTING. So don't underestimate the need to take time for yourself.
"Love As Thou Wilt"