I have been in Waterfall (current company) model and agile structures and some strange ad-hoc hybrids and requirements capture has always been the weaker link in the chain.
There are no magic bullet here and I do not think a good word template however much time is speant trying to get it right will do the trick. But it is not hopeless. The main problem here is not only you do not speak the same language but they will not know how "shallow" or "deep" they must go into.
also, very often, they will not know exactly what they want (in my opinion one of the fundamental flaw of the waterfall model, but this is another debate) and will cover their ignorance with painfull amount of documentation.
There are two situations I have worked in that made the whole requirements capture pain go away.
1 - Usability testing on iterative prototypes. This approach works good in an agile setup but it can be coereced in a waterfall if the prototypes remain in the specification phase. Get a prorotype of the user interface for the functionnality they are after. Since this is the part they will be interacting on then it will help make their ideas clearer and will help you understand better whas is it they need.
and/or
2 - Actually sit with the customer and extract the requirements with them. Requirements are engineering documents for engineers to understand. I have rarely, if ever, seen requirements document correctly written (witht he PoV of engineering that is) if it is done by non-engineer. Having one to sit with the end user (or marketing departments) and write the document for them, with them will save you oogles of pain.
The main secret here is dialogue, nothing will beat a good constructive discussion with them. With it you should get enough information to get started. Once started then go back and test with them to fill in the blanks and stay on target.
But to expect them to give you a document that covers everything and anything you need to know to build the system is bound to fail, there is just no bridges for the engineering chasm that split you and them appart.