I'll add, since my original definition of 'emotional exhaustion' resonated with you, OP, that after a while of not feeling anything, you get royally fed up with it - and then it starts feeling like depression. That's what happened for me, anyway. Feeling depressed is a natural result of boredom, and that's what you have. No interest in anything, ie everything is boring.
Take very good care of yourself, and remember that if you're holding yourself together so that other things don't fall to pieces, that's not an infinite resource. You have to make sure you don't fall to pieces, and, if other people are depending on you, that makes your wellbeing even more important.
Do you think you could talk to your husband and let him know what's happening for you? You're clearly worried otherwise you wouldn't have posted, and you'll need his support on this. Keep in mind that looking after yourself isn't selfish, it's going to ensure you can keep doing all you need to do, for everyone, not just yourself.
And be accommodating. For me, when mine had turned into actual depression and I went to the doctor, she told me I was 'a textbook case'. This was very reassuring, and when I said 'Can it be fixed then?' she lightheartedly said 'Of course!'. That, in itself, was a huge bolster for me.
So, I'll say it to you, too. There's nothing odd in how you feel. You're completely normal, and having a completely normal response that many have in normal life, but even more so at the moment. Drop the guilt. You're not doing anything wrong, and just because you have a cushy job, that doesn't mean you're obliged to be happy. Somewhere along the line, your individual needs are not being met. Give yourself a big hug and a hot chocolate, or something, and have a chat with your husband about how you need to find a way for life to be a bit softer on you for now.
We're all delicate and overwhelmed at the moment. You're not alone.