Huh? In typical rock, the bass drum is on 1 and 3, and the snare drum is on 2 and 4. Think "boom...bap...boom...bap". 1 and 3 are the downbeats and 2 and 4 are the upbeats.
Maybe you are thinking about counting eighth notes on the high hat -- in that case the bass drum would be on the first high hat hit, and the snare would be on the third. However the counting should always be on the quarter note, i.e., two high hat hits per count -- "One and two and three and four and."
No, I'm talking quarter notes in 4/4 time here. Bass drum on one, snare drum on 3 and timekeeping hand playing on all four quarter notes.
In your "boom...bap...boom...bap", the ellipses are quarter-note rests. Listen to any simple rock tune, say, AC/DC's Back in Black. With BD == Bass Drum, SD == Snare Drum, HH == High Hat, what you get is:
Note | 1 2 3 4
-----|-----------------
HH | x x x x
BD | x
SD | x
Maybe you are thinking about counting eighth notes on the high hat -- in that case the bass drum would be on the first high hat hit, and the snare would be on the third. However the counting should always be on the quarter note, i.e., two high hat hits per count -- "One and two and three and four and."