Katiejon, in my opinion if a spouse cares at all for their partner they would be more interested in seeing that he or she feels secure than in maintaining some sort of secrecy regarding anything, be it finances or where they're going for a pint. While I know that it is VERY important that you know financially where your family stands, it's equally important that you consider the overall respect and concern that your DH has for you as a wife, mother, and person.
As a side note, I worked for 30+ years in the US's OAP program. You would be absolutely SHOCKED to know how many spouses (usually wives) know little to nothing about family finances and are either shocked to discover the lack of income left for them and/or their young children or are left destitute upon the death of their partner. I can't count the times I heard 'But I can't live on that! What am I going to do?'. I saw more than one widow lose her home to foreclosure or lose her comfortable lifestyle for a lifestyle of penury or dependence on her children. Even though I always earned as much or more than my DH, I always made sure that BOTH of us knew what the other earned AND what provisions had been made for the other in the event of death. The fact that your DH refuses to discuss these matters and has, indeed, arranged for his savings to go elsewhere would be frightening to me!
My sister (SAHM), on the other hand, was content to let her DH handle the finances. As long as she had money to spend, she didn't care what was in the bank or how much BiL earned. She didn't know he had lost everything in the '08 property bubble until they were so deep in debt she had to call our mother in tears to borrow funds to keep them afloat. He was too ashamed to tell her and so let her keep spending, knowing that they didn't have funds to cover the debt.
Financial transparency is of paramount importance whether it be in government, business, or family matters!