Word for "pertaining to the interface"

Yes you could, interfacial is a word, and it can be used in the context you have described:

interfacial

2. of, relating to, or of the nature of an interface. - dictionary.com

However it would be far more natural to simply say:

"The design shall be adjusted to account for the program's interface limitations"

or, slightly better:

"The design shall be adjusted to account for the interface limitations of the program."

However, your example sentence aside, I think what you mean to say is:

"The design shall be adjusted to account for the interface limitations of the system."

Because it is the system that has the interface, and not the program.