nothing is normal, because there's no such thing as normality. sanity is when you avoid tripping over your emotional shoe laces. there is something more properly called conventionality which the less intellectually active, let us say, mistakenly refer to as normality. but it is a very big mistake to make this assumption, which there is nothing natural, moral or healthy about doing so. there are certain constraints in our waking world, which are abscent or entirely altered in what we experience when dreaming. there is real, even potentially lethal risk, in loosing recognition of the difference in these. is it possible to walk, or otherwise function, uninterupted between both world/states? while extremely unusual to do so without mishap, it is not inconceivable. there are also some overlaping conditions between both states, such as halucinatory states of extreme fatigue and of course so called lucid and the out of body. i'm guessing something of one of the latter is what the question alludes to.
Similar to when air meets the water and water meets earth. To call the 3 things separate is inaccurate, they just have differing densities and arrange themselves so. What we perceive as a boundary is more of a meeting point, equilibrium. When you climb out of water(wake state), you remain wet for a while(dream of waking influences). Vice versa, except air(dreamstate) wants to escape the density of water faster than not("Woh, that was a weird dream! glad I'm back in reality!" - proceed to forget the dream). ^ A vague model for the conventional perception of reality. Things can get weird, but no worries. Breathe clearly and you'll find your way home. It's worth exploring imho
yes, deep slow breaths. this blurring of separation of dream state from the way the world we're awake in works, is what the word 'trance' and 'trance state' used to mean. before someone decided to use it as a name for a kind of music. just don't throw yourself at the ground with the idea you might be able to miss hitting it, while you're awake. there's probably a world somewhere, that you could get on a buss, stark ass naked, and not have to pay a fare, and no one would even notice or care. it just doesn't happen to be this one.