trouble printing business cards on HP3650

I purchased a packet of the business cards, i.e. an A4 sheet of
cardboard that is perforated, so you can tear it into 10 cards.
It was said to be for "inkjet printers". When I tried to
print on a HP3650, the printing is about 15 mm in error.
When I did trial runs on 80 gsm paper, the printing was a good
match to where the perforations are on the business card blanks.
So I went to printer properties, and selected premium matte
photo paper - and then it's about 10 mm in error. If I select
greeting cards, it's only 5 mm in error, still useless.
Then I tried a sheet of 210 gsm card (without perforations,
like the business card) and guess what: the printing comes
out in the correct postion, even if I select plain paper in
printer settings. So it seems the HP3650 can handle the
thicker stuff, but not the business card blanks with all the
perforations.
Mind you this printer is not so good for envelopes either.