When I have an album that contains both sub-albums (maybe just one) and also images, sometimes they appear consecutively and sometimes the album(s) appear on the first page and the images start on the next. Would it be possible to have the option as to how they are displayed, and with the default of the sub-album(s) and images appearing together?

Options ->Theme -> Enable transition page

you might need to adjust min and max numbers to work well with your content

I've been trying to resolve this for over a year, with various combinations of Transition Page Enabled or not, and different numbers of min and max image thumbs, but nothing seems to work, but with one combination I lost the images altogether.
I'm using the ROMA theme with max 24 albums and 36 images per page.

A theme named ROMA is not known to us. Perhaps try a standard theme and see of the transition works with that. If it does whoever who created your theme need to work on it.

Also make suere your are using the current Zenphoto release as its transition page options allow setting such values.

ROMA is derived from ZPbootstrap, so something that works with the latter would be worth trying on the ROMA theme.

The options should work with any theme unless it does things off the standard or overrides anything. So try the Basic theme first. I don't know if zpBootstrap does things differently in some place.