The problem you may be having is when you select multiple checkboxes, you get a return separated list. Put a second checkbox field on the layout, but make it a text field, and make in about an inch wide and 4 inches tall. Watch what happens to that field as you check and uncheck boxes. The order of the list changes. If you're trying to match this on both sides of a relationship, and the boxes aren't checked in the same order on both sides of the relationship, I would think this would fail.
Can you post a sample file or some screen shots of what you are trying to accomplish. Also it's very helpful if you use exact words to describe what you are doing instead of first table, second table, field one, etc.
Also your title says field contains part of text, but nothing is mentioned about that in the post
You may want to also research 'multi key' to see if that is something that is more in line in what you are looking for.
The multi key search solved my problem in a much easier way, thanks a lot.
Sorry for the unclear post earlier.