Although the trust does provide British Sign Language (BSL) interpreters and interpreters in 30 different languages to its patients, the couple cannot have one because Mr Bassett is not the actual patient.
He now fears something might go wrong at the birth that he will not be able to understand. Mr Bassett said: "I feel discriminated against by the trust.
"BSL has been legally recognised as an official language since 2003 by the Government.
"It's unfair for us having been caused so much stress at an important time in our lives and I have missed out on much of the experience, which we can never get back."
Mr Bassett, who was born profoundly deaf, is used to having interpreters provided by other organisations, including at the bank, doctors and dentist.
Although his partner Toni Burrows can sign, she isn't fluent in medical terminology and the couple fear she may be in too much pain while in labour to be able to communicate with him.
After making an official complaint, a BSL interpreter was provided by the trust at the 12 and 20-week scans at Hull Women and Children's Hospital.
Miss Burrows, 31, who is 36 weeks pregnant said: "We feel completely let down.
"It's really frustrating and has put a shadow over the whole pregnancy.
"We were delighted we got one for the scans but still felt we were being dismissed and treated unfairly as we needed an interpreter at all the appointments and especially the birthing classes and the birth.
"Adam is extremely upset and very frustrated as he feels he hasn't been given the opportunity to fully experience the pregnancy as a first-time father.
"The midwives are outraged we have been denied interpreters and have tried to help us as much as possible."
Miss Burrows has presented the trust with a Royal College of Midwives document, entitled Reaching Out: Involving Fathers In Maternity Care, which clearly states the NHS policy is to increase engagement with fathers and encourage them to be involved in maternity care.
Miss Burrows said: "The document given to me by a midwife came as a shock as, so far, Adam hasn't been given full opportunity to be involved in the pregnancy and I feel has missed out on an awful lot of things.
"At the birth, the interpreter wouldn't have to be in the room all the time, but we would need one in case something went wrong, so Adam could be kept informed."
Hull West and Hessle MP Alan Johnson has now written to the trust's chief executive Phil Morley to find out why the couple cannot have an interpreter.
A spokesman for the trust told the Mail it does "provide interpreter services for all patients who require them".
However, when the Mail asked whether there would be one for Mr Bassett, the spokesman said: "In this case, we have funded a BSL interpreter for the father at the 12 and 20-week scans."
He said he was unable to discuss the case further due to patient confidentiality.
