Tile over laminate/vinyl

Just a couple questions:

My wife and I are about to tile our kitchen and hall floor (167' total) with ceramic tile.  The house is a Cape style built in 1955, when we moved in we ended up pulling up two layers of carpet and found another layer of vinyl (laminate?) flooring underneath.  I've already tried removing it by hand, and by sawz-all with a scraper attachment that would really only take up the tile by taking chunks out of the floor.  Would it make sense to just tile over right over whats already there?  We're also trying to figure out if it's worthwhile to lay down a cement board layer, we're just worried that the 1/4" cement board plus the width of the tile itself is going to add too much height to the floor to transition into the dining room hardwood floor which is right next to the kitchen.

Any thoughts and suggestions would be very much appreciated!

Thanks!

http://www.lowes.com/pd_73041-1813-97518283323_0__?productId=3191801&Ntt=mesa+rust&pl=1&currentURL=&facetInfo=

There is more to consider here then just can you......

Let's start by figuring out if there is a 1/4" luan (plywood) under the vinyl flooring.? If not is the vinyl laying directly on the sub floor, and how thick is the sub floor.?

Do you have a dish washer.? If so how much height adjustment do you have.?

Now let's find out how much floor deflection you have. This will let you know if it's okay to lay the tile without a chance of it cracking, or if you need to beef it up. Clink on the links below and fill in the blanks.......

http://www.awc.org/calculators/span/calc/timbercalcstyle.asp

http://www.johnbridge.com/vbulletin/deflecto.pl

come back and let us know, we will take it from there, okay.?