I had no bills in my ILR app. (I in fact had no joint mail at all). I had bank statements, mail from my GP telling me to come in for an appointment, a letter from the DVLA, and letters from HMRC. For my husband, we had the standard household bills and council tax and etc, there were no issues at all.
Just make sure you have enough official mail for both of you, from a variety of sources, spread out over the time you need for the ILR.
x-posted with Dr.Super