Assume they will check it every time - if you need a visa make sure you have one. It may be that it is not checked but you definitely don't want to travel without having the proper documentation.
I agree with what Michael has said.
If you have a valid passport and visa why do you need to know?
How often do they check your visa?
Once each way I would have thought.
What nationality are you?
I can't recall a passport check on or off the ferry but its been a few years since i have been on one
Depends on your method of travel I think.
Travelling backwards and forwards in your own car they do not check.
Foot passengers and coach passengers are often checked. My daughter was on coach once and two young foreign lads were 'removed'. They did not come back.
We last travelled over a year ago this month,out from Birkenhead to Belfast & back from Dublin to Holyhead,we had to laugh when we got back home & saw a new series on TV where they claimed that everyone was checked/searched both going on & coming off all ferries,nobody came near us on either journey,luck of the draw I guess but as long as your documents are in order you should have no problems.
I wouldn't expect checks between Birkenhead and Belfast as you are not crossing any international borders.
I wasn't surprised to be stopped coming off the ferry in Dublin because we were crossing an international border, and the CTA - strictly speaking - only applies to British and Irish citizens. They have been checking passports at Dublin Airport for some years, so checks at the seaport should not come as a surprise.