If the position is pretty much dedicated to doing work for the client, full-time, then it's not that unusual at all.
Instead of wasting the time of hiring someone they think would be great for the client, then possibly having the client reject them for some reason, this puts part of the onus on the client to accept the new hire, since they had direct input into selecting the individual.
I wouldn't say you'd do anything different. While your employer is acting as an intermediary, it's basically an interview for a job that will be done for the client. The job, itself, won't be that different and the parameters of the interview will be the same.
The client company would merely remove themselves from the process once you move further along and get into the logistics of on-boarding with the employer who signs your paychecks, so you'd just be looking to stick to the technical nuts and bolts of the work for the client, and their work environment, and assume the contractor-related discussions will be handled separately, in a future meeting with just the actual employer, once the client agrees that you are the best thing since sliced bread.