I have also the same problem.
It seems that you need to specify the appropriate model for each partition, and specifically a binary model for the binary dataset (e.g., MK), otherwise it cracks.
e.g.
#nexus
begin sets;
charset part1 = DNA1.fas: *;
charset part2 = DNA2.fas: *;
charset part3 = Binary.fas: *;
charpartition mine = GTR+F+I+G4:part1, GTR+F+I+G4:part2, MK+ASC:part3;
end;
This will work.
But the real problem is that the command "-TESTMERGE" will not work. So, I do not see how it is possible to have, at the same time, the binary dataset with the binary model (and perhaps the ASC correction if you need it) and test the partitioning scheme with PartitionFinder for the remaining datasets...
Also, I do not know how to combine partitions included as independent alignments (or parts of alignments) in the NEXUS file, since between partitions you can only use "," to separate partitions or ";" to end the block. I mean, you cannot use "part1+part2", or "part1_part2", etc.
The only solution would be to run a previous analysis without the binary dataset to test the partitioning scheme for the other datasets, and then manually arrange the partitions to comply with that partitioning scheme. Very inconvenient, particularly if you have partitions by codon position, since you would have to split each codon position, then mergin them with others, etc. Or merge everything into a single long alignment, and then call the partitions as usually done for other software, but then the great versality of IQ-Tree for using independent alignments would be lost.
Did you reach any other conclusion on this issue?
Best wishes,
Juan Carlos