No the street in front of your house is not private property and belongs to the public.
Anyone who wants to drive down the street in front of your house can do so legally and they can also park in front of your house in the street as long as they are not blocking a mailbox or fire hydrant.
However if the street in front of your house has been vacated by the city then it could actually be your private property which was a case on dirt road in front of my old house.
I found out through my deed to the house that I had owned at least half the street out to the middle of the road and the homeowners on the other side owned the rest of the side of the street.
So in that case part of the street could be private property.
But if the street is not vacated and it's not listed on your deed then the street is public property and people can park on it legally or drive down it legally.