You are right, the solid bodies need to be cut from the fluid domain for generating region interface. Interfaces are generated between overlapping faces. If there are no overlapping faces between the 2 physics regions, there won't be any region interface generated.
Secondly, if you look at the "Region Interface Generator" there is a message saying that several faces are candidates for more than one region interface. See below snapshot. This means that one face is a part of multiple overlapping regions. All such faces get ignored in region interface generation. That is why the region interface generated between thermal physics region is showing only a few interfaces.
To overcome this issue, you need to spit faces where bodies are touching each other. The quickest way to achieve this is by imprinting. To do this, go to Geometry task and edit the geometry. In Modeling window, go to Prepare tab and click "Imprint" tool. This will highlight all the possible locations in the model. Click the "Complete" button to complete the operation and create imprints. Once done, close the modeling session. Go to flow task and delete already created region interfaces. Now regenerate the region interfaces using the interface generator. You should now see several interfaces within the thermal physics region.