I understand how you feel - my husband always feels responsible about finances even though we are both self employed. If you do not talk to him about it you are protecting him from the stress of feeling that hes 'not doing good enough'.... but you are taking on the anxiety about it alone... So you need to address that anxiety - where does it come from? when did you first feel anxious about money - or having 'enough'? Often this goes back to childhood .... as most things do! Perhaps you could address your issue with the anxiety and then not need to tell your husband. Get to a place where you feel that you will both be ok whatever happens... we mostly worry about the stuff that if something really major happened - earthquake, war, etc - would go by the wayside. The really important stuff is - are we healthy, are we happy, have we got enough food today....
Bu the flipside is that your husband will feel responsible and be stressed about the subject anyway - by talking to him you may be doing him a service - he has not got to shoulder it alone.... he might feel bad as a provider but will he feel more supported as a partner?
Only you and he can sort this out... it is a thorny problem. Both of you deserve to be happy, and both without undue stress - or at least stress about stuff you can control....
My husband and I do talk about it - he still feels like the provider and main responsible person....(equality has not got us far!) so still feels somewhat stressed when finances are stretched... But he also knows that when push comes to shove - i would walk away from my home, my family and my life -with him - because HE - not the life we have - is the important one..
It helps that we enjoy cycle touring - when you pedal around a country on a bicycle with everything you need in 4 panniers - your shelter, your food, stove, clothing...you realise that you have everything you need - all you left at home - is extra!