Technically dinosaurs are classified in Reptilia. By extension, birds are as well. (Though from what I've heard there might be a bit of confusion regarding the real classifications of some things in Reptilia, especially with crocodilians being more closely related to birds than lizards.
Dinosaurs are classified as their own species. They are dinosaurs. In a general sense (and I mean extremely general) reptiles, birds, and dinosaurs all more or less developed from the same ancestors. They are related, however, they are separate from each other. Just as we are separate from say a spider monkey. At some point in our past we shared a common link, but we are very separate species.
If you consider the Darwin's theory of evolution which happens to remain in the realm of theory... besides the huge gaps they have yet to fill in that theory. Dinosaurs could very well have been reptiles, but at the same time, they could have just been mammals with scaled skin.
It bugs me when people confuse the meaning of the word theory.
"A scientific theory summarizes a hypothesis or group of hypotheses that have been supported with repeated testing. If enough evidence accumulates to support a hypothesis, it moves to the next step—known as a theory—in the scientific method and becomes accepted as a valid explanation of a phenomenon.
When used in non-scientific context, the word “theory” implies that something is unproven or speculative. As used in science, however, a theory is an explanation or model based on observation, experimentation, and reasoning, especially one that has been tested and confirmed as a general principle helping to explain and predict natural phenomena."
Essential difference .
There's no "huge gaps" in the theory of evolution. The theory works (else it wouldn't be an accepted scientific theory), it's elegant and beautiful: [link]
No, they weren't. Reptilia includes Dinosauria, which includes Aves (birds). You are trying to classify them with what you know of modern reptiles, which is like trying to classify what you know about dinosaurs with what you know about birds.