I think it is great you are taking an interest now. Embrace it! 
Â
I have a degree in finance and have worked in many different facets of money management. I've also helped friends and employers get their financial acts together. Currently, I am helping my DD's school with fundraising and proper fund tracking.
Â
From my years of experience, my best advice is to start with paper and pencil. The physical act of writing it all down tends to make it all feel more real for most people and it is easier for the average person to understand that way. You can choose to work from past records or you can choose to start with the present. Doesn't really matter for your situation. It also doesn't really matter for households when you define the expenses (date incurred or date paid). It definitely matters for business expenses, though. There are official accounting methods for all of this stuff, but it isn't that important for the average household.
Â
Once you get a feel for your family finances on paper, then you can explore other options. A simple spreadsheet, Quicken, and a whole big list of other options. Quicken is awesome, but I don't recommend using it right off the bat. It confuses people who are just learning the basics.
Â
When I work with individuals at the stage you have described, I have them write the dates and amounts of each paycheck for a given month at the top of the page (incoming). Subtotal those. Then, list each bill that is paid with the date and payee (name of company) and amount (outgoing). Subtotal those. Subtract the outgoing money from the incoming money and circle it.
Â
I still have index cards from when I first started this eons ago! I moved to a spiral notebook the following year and then to a computer. Computers were not nearly as available as they are now and I am not advocating two years of tracking first! 
Â
If someone is already saving, then I have them write it in the appropriate category: incoming if it is pretax or you never see the money (separate deposits, for example); outgoing if it comes into your checking account and then back out to a savings account (of any kind, these are general terms) whether it is automatic or you initiate it. You need paycheck stubs in hand. I encourage people to write the gross salary and subtract out all the items that come out of their checks before they see the money (taxes, 401k, healthcare, everything). For most people, it is easier to have all this in the incoming section because they only see the net effect of all this stuff. Once you know this info, though, you have more control over it and it becomes more important to see it in black & white.
Â
In the beginning, I don't recommend categories. Just write the date, name of company paid, and dollar amount. A couple months of this and most people get it and are ready to analyze further. Some folks never need or want to take it any further and that's okay, too. Incoming and outgoing really is the basic information. Everything else is extra. Your DH's "one pot" method actually will make your task easier. Once you understand it all, you may want to influence that strategy differently, but it is a good method overall for a lot of people. Simple can be best.
Â
Best wishes!!! 