While the carrier is held back, always push the loose handle back forward and click it in. The spring-loaded latch must engage to keep the handle locked in. If the latch doesn't lock the handle into the receiver, something is wrong.
As others have stated, yes it is normal. The charging handle only moves the bolt carrier to the rear, as it is not attached to the bolt carrier. Since the bolt carrier and the charging handle are not attached, you can not push the bolt carrier forward... the charging handle moves freely forward. This is different from other rifles that have an operating rod, and the reason the Army wanted the design change to include the forward assist.
I told a guy I was shooting with yesterday to lock in his charging handle. He didn't listen, and he broke the charging handle when he dropped it on the table. He was pissed, but he wouldn't listen.