The answer is somehow lenghty. But....
We have bows of ugrofinnish origin, some siberian and rusian bows all made as complex wood composites. Some of these are early mediaval, some even older. That means that the technology was there.
If you are asking if a method of glueing two pieces of wood (backed bow) existed or was used on the western scene e.g. on english bows -
At the end of 15. century the yew wood became scarce and the quality dropped. So the bowyers looked for means of using yew staves with bad or damaged sapwood.
This is done either by backing yew heartwood with yew sapwood in case you have two staves on which opposite is bad of quality, or they backed yew with a single growth ring of elm or ash.
(I can write you method how to obtain such a backing strip).
Two such bows did survived, both are in archery hall in Edinburg, one is from 16. century and another from 17. both ash backed yew.
Howewer technology was present much earlier than that, take a look on tudor lances glued from many strips of wood.
We also have a letter from french minister of artilery to the chief of the gun and bow maker guild in Paris "For to make more of the new bows from many pieces of wood as they break less than the ones from one piece".
Was it a standard? Not really. A soldier would have single stave yew bow and the ones fighting in france nothing else, as they were elite. Whitewood bow was never option for professional soldier.
This is one of things you have to keep in mind also, that mediaval bow was very heavy and the technique of drawing different from flimsy sporting draw we see today iat many a "medieval archery competetion."
I think of backing as thin as 2mm too thin - It all depends what you want to back, but 5-6 mm is about right. Two woods belly/back should complement each other in strenght so if you have very hard and dense belly as some of tropical hardwoods are, you need thicker backing.
This is Ipe backed with hickory longbow I made two weeks ago, it pulls like 60#/30´´ and it sends 30 gram arrow 230 meters afar.
http://sweb.cz/hawkwind/noveipe.JPGNot a mediaval bow indeed as this is made like sporting victorian longbow, but extreamly good in performace.
This is single stave yew bow also made by me for comparition
http://sweb.cz/hawkwind/mrselfyew.JPGYou can see all the nice character of the stave which is so often present on medieval paintings.
Sorry for english, I can read polish, but not write, unless massacre your language.
Jaroslav