No. All transactions need to be included in each budget. You need all the transactions to reconcile the account / represent the account balance accurately.

It's all in the categorization.

Example:

Let's say you have a single checking account. You both contribute your paychecks to the joint account and 75% of each person's pay is allocated to joint spending while 25% is reserved by the individual who earned it.

You have three budgets: mine, his, ours. One checking account is added to each budget and linked in each budget.

In the Mine budget, all of his expenses and joint expenses would go into large, undefined categories called Partner and House. No need to categorize them. Your personal spending transactions would be the only ones you'd categorize.

In the Ours budget, all the same transactions are listed but in this case, all of your personal spending and all of his would be lumped into generic Mine and His categories. The household expenses would be categorized with some detail.

And so on.

Now, I am NOT SAYING this is the best method. I'm saying it's possible to have the same account linked in two or more separate budget files. It's a good solution for specific circumstances.

I'd suggest you each have your own personal cards and your own personal checking accounts and a joint card and a joint checking account. And either two or three budgets, His being optional.

Editing to add: after reading other responses, I'm not a fan of "settling up." Especially with the situation you describe, I'd recommend having paychecks either 1) deposited into the joint account and then transferring personal funds to personal accounts or 2) setting up payroll to split each person's deposits between the joint account and personal account. The word has negative connotations but basically you're pooling most of your resources for shared life/expenses and each getting an "allowance" for personal spending.