I really feel for you, my DH and I went through a similar period where coincidentally we both went through a period of work stress (for different reasons) and I really think it was much much worse than if just one of us was going through it at a time, we had long circular conversations into the night not always really listening to one another and the stress of our own job worries was only compounded by worrying about the other person. We came out of the other side fine but it wasn't a happy time.
Agree with what others have said about it being helpful to understand your finances and what your minimum necessary income is - maybe try and take a step back from your current incomes and lifestyle and how important it is to maintain that -e.g. it is easy to get trapped into a bit of a treadmill of paying a large mortgage or rent in an expensive city or area and then needing to get a high paying job to fund it, then not being able to move away from the city to do the job... but it can be possible to take a step away from both although it won't happen overnight (or by Christmas!) and can entail big lifestyle changes/sacrifices which can be really hard to think about when you are stuck in the daily grind of trying to make ends meet.
It does sound like something needs to change, but if at all possible I would avoid quitting either of your jobs without something else to go to or a clear idea of what your next steps will be. I know it's so hard to try and get perspective and think things through calmly when you are in the middle of a massive stress but equally acting impulsively is not always a good bet and I can see that your DP/H could feel even more stressed and trapped by his job if he is forced into being the main breadwinner by you unilaterally quitting yours (or vice versa).
Have you got any time/space to reflect, separately and as a couple on why you are feeling so stressed, what it is you want to get out of work and what kind of lifestyle you want (and therefore how much money you want to earn, hours you want to work, where in the country you need to live) and from that what you would want your next steps to be? Have you got any time off work coming up, can you try and use this to really try and do some good thinking and proper talking (not stress bickering)? Maybe even go away if that's possible to get some physical distance from work? As others have said talking to someone external (e.g. a careers coach, counsellor or even a family member or friend who is a good listener) can also really help you get your thoughts in order.