Op, honestly you've actually just done the hardest thing. You've opened up about it and admitted that this is a problem and you aren't coping.
Honestly you need to tell your dh, if he cares about you and is as lovely as you say then he'll be worried and want to support you.
You've been through a massive and very traumatic loss. It makes complete sense that your brain has tried to find a way to cope and get help for itself if you previously weren't able to find the words or the space to do that. These wounds always find an out, you are not abnormal in that respect and you are not alone. I personally know a couple of people who dealt with traumatic loss with theft. It's more common than people talk about.
That being said, there's no reason for you to feel like you need to end things or to continue feeling this way. You are hurting and you deserve support.
The best thing you can do is speak to your dh and tell him honestly that you're not coping and what's been happening. He might react to that and he might struggle to understand but I think you need to be prepared for that initial reaction and allow him a bit of processing time. This will be new for him, but you've had time to think about it.
The next step is referring yourself for grief counselling/ addiction counselling. I would be trying to find someone who specialises in both ideally and who is accredited. Both are connected but the drinking and stealing are a symptom not the root cause so trauma and grief work are key. Speaking to your gp would also be important as they might be able to refer to adult mental health services for specialist provision. There's usually a waiting list but if you have the means maybe you could fund privately initially or ask for advice on free services locally. You also probably need a proper assessment for the likes of ptsd which would be very understandable given what you've been through.
Op I think it's really important that you hear that you aren't doing this because you are a bad person, you're hurting and struggling with your mental wellbeing and yes, you do deserve to be treated with grace and respect. I know it maybe sounds a bit silly to say but I'm honestly really proud of you for opening up about this because I know it's really hard to do and scary because it's the first step towards changing your life. But you can absolutely get yourself back on track. People do it all the time with the right support. It's not easy but it's not impossible and the future really doesn't have to look or feel like what you've been experiencing. You have an opportunity here to start a new slate and you really do have what it takes.