You are asking about two things:
- from the viewpoint of Earth itself
As an observer passes the event horizon, the observer experiences nothing special (except for spaghettification). In reality, the observer might not even realize he passed the event horizon.
If you disregard the effects of extreme curvature (on the different parts of Earth, and on its rotation), then the Earth would just pass the EH and nobody on Earth would notice nothing special (OK, the Sun and anything else on the sky would disappear).
In reality, if Earth would collide with a BH, the first thing to be pulled towards the EH is the atmosphere, then the liquid parts, oceans, then because of the extreme curvature, even the shape of Earth would become spaghettified.
- from the viewpoint of a far away observer, away from Earth. In this case, the observer would just see the Earth frozen on the EH forever, because of GR time dilation.
You might be asking something different. If you are asking about two different observers on different parts of the Earth, then this could be interpreted as two co-moving observers.
In this case, two co-moving infalling observers would experience the switch between the time dimension and the spatial dimension (pointing towards the singularity). Time would just be the dimension that leads towards the singularity, and the spatial dimensions would take the interpretation of time.
After your comment, you are asking about what happens when there are two people standing on different parts of Earth. One observer already passes the EH, while the other not yet. The observer who did not yet cross, will see the other one frozen on the EH.
But this time while the observer sees the other one frozen is not infinite. Why? Because the observer who sees the other one frozen on the EH is moving towards the horizon too, and will reach it in a finite time. At that point, both have reached the EH, and will be inside of it. From there, they will be regarded as two comoving infalling observers.