Hi qwerty12321,
Yes! In the sentence you cited, the adjective "beautiful" refers to both the house and the kitchen.
They have a beautiful house and kitchen.
The reason this is technically correct is that the adjective is referring to a pair of things: the house and the kitchen.
If you add the article "a" in front of the word "kitchen," you break up the pair and confuse the meaning of the sentence:
They have a beautiful house and a kitchen.
The meaning of the sentence is confused because we don't really know if the author means that both the house and kitchen are beautiful, or that just the house is beautiful, and they also have a kitchen (which must be ugly because it was not paired with the beautiful house).
In general, the adjective (or adverb) applies to all the elements in a group (a pair of things, or triplet of things, etc.). When you break up the group, as above, you break up what the adjective (or adverb) is modifying.
