I am trying to match the height of the laminate floor in my family room to the intended kitchen floor which I will have tiled. Unfortunately, the subfloor is OSB layed on a 16 in span joist and the contractor said I will either have to lay a 3/8" plywood or spend on a 1/4 inch backer board to make the foundation sturdy. That will make the height of the tiled floor about 1/2 inch higher than the adjoining family room floor. I read about the ditra membrane and want to know the finished height after a 3/8 inch tile is layed down. I am trying to minimize the finished height as my laminate floor is 5/8 inch. And will this be sturdy enough for foundation?

The membrane itself is 1/8 thick. WIth a 3/8 tile plus ading your mortar underneath you'll be pretty close, if not exactly at the same heigth. As far as strength, that really depends on your subfloor. If this is a newer house I'm sure you'll be fine. Can you see in your basement how long the joist are unsupported ?

Ditra does nothing to strengthen a floor. It's an isolation membrane (only), and an excellent one at that.
Randy is rght, how long are the joists under the floor between supports? If they are around 14' or more there may be a problem.
Also, Ditra over OSB??? I wouldn't consider trying to bond anything to OSB.

The most important thing to take into consideration is the strength of the installation and THEN the height differences of other rooms and how to resolve. It isn't unusual or wrong to have varying heights (within reason)

I wouldn't worry about bonding Ditra to OSB. The shear mass of a 3' wide strip of Ditra is not going to pull OSB flakes off the subfloor.
If you tried to lift a pc of Ditra off OSB after it's cured, the plastic will separate from the fleece first.

Mike is right about the heights. They are your least concern. Having the right subfloor support and correct tile underlayment is more important.

I have one of those 'great rooms' where the family room and the kitchen are in one room and I have laminate on the family room side. Under this room is 4 ft crawl space. The gap in the joists is 16". It is an 8 year old parklane house and the transition strip will be about 13 ft long. That is why I am trying to minimize the difference in height as much as possible to avoid tripping on the higher floor. So the ditra membrane is not going to help me any? I am almost tempted to have the subfloor stripped altogether down to the joist and just lay 5/8 or 3/4 plywood but that is a big job. Any other ideas?

Two things:

1. What is the longest unsupported span of the joists where the tile is going?

2. What is the thickness of the OSB?

I think this will be a solution to the heights, TD ProBoard this product can applied straight to the floor joist then tile (total thickness is less than 1 inch)

It called TD ProBoard and I had a good success with this board when getting in to situation where I need my tile floor to be lower then normally I would get applying plywood and cement board