Just break down the two terms to see the difference and, consequently, the relationship.

A mental model is just UX jargon for "the picture I have in my head of how I expect this thing to work". An "information model" or domain model is the way the designer of the system intends for it to work.

For designers, it's important to recognise that whatever you design, however well you design it, people will end up forming their own picture in their heads of how they think it works. And that can differ pretty substantially from what you as a designer had intended.

Great designers therefore are able to intuit and predict the ways that their domain model will end up being translated by users of the system into different pictures. Being able to do that is usually a function of experience and talking to hundreds of people to learn the patterns that lead to that translation taking place.

This is why [domain-driven design](http://en.wikipedia.org/wiki/Domain-driven_design) is a great methodology: it standardises that approach and helps you learn to map domain models to mental models more effectively.

See [Mental model vs conceptual model: what's the difference?](http://ux.stackexchange.com/questions/9417/mental-model-vs-conceptual-model-whats-the-difference) for a similar question.