Due to it being a joint account it can be allocated to each of you to report. The allocation can be 50-50 or any combination. Can be based on income levels or who put most of the money into the account, so 100% could be on one return.
There should be a primary SSN that the 1099DIV is associated with, and IRS will match that with whoever's SSN it is. So whose ever return it goes on, or does not go on, make sure 100% is reported to IRS between the two returns. Also due to IRS matching this document, you may get a letter a year or two and may to explain to them, how it was reported.