Wow! I'm really, really surprised at the number of answers on here advising parents not to tell their kids that they are suffering with anxiety/depression. I thought that we had moved on a lot further as a society than that, but perhaps not.
My mother has struggled with chronic mental health issues since I was a young child. I wasn't formally "told" about these issues until I was a young adult but I sure as hell knew that there were serious problems way before that! It is utterly naive to think that you can hide this kind of thing from a child who is living in the same house as someone suffering with these issues, and ridiculous to think that, in doing so, you will somehow burden them. On the contrary, it's far, far better to explain to a child that depression/anxiety is an illness and that medical intervention is sometimes required to treat it, as that can help to take the pressure off the child who might otherwise feel responsible for things better.
My mum did not share any information about her mental health issues with us when we were children, precisely because she wanted to protect us and not burden us, but in avoiding the topic, she made the burden infinitely greater. I was painfully sensitive to my mother's moods and worries when I was a child, and I spent most of my childhood/teenage years trying to "fix" her. I felt a huge weight of responsibility for her unhappiness and her worry, and yet couldn't talk about it because I knew that it was somehow considered a taboo subject. It would have been so much easier if she had just talked to us about it, instead of trying and failing miserably to cover it up.
Please, please do tell your kids what's going on. They will know that something is wrong in any case, don't kid yourself that you can cover it up. You don't have to share every detail, but they have a right to an age-appropriate explanation so that they know that it isn't their fault and so that they know you're getting appropriate help.