There's a labeling problem here. E is an event. The extra information you're updating on, the evidence, the thing that you are certain of, is not "E is true". It's "E has probability p". You can't actually update until you know the probability of E.

What the joint probability give you is by how much you have to update your credence in H, given E. Without P(E), you can't actually update.

P(H|E) tells you "OK, if E is certain, my new probability for H is P(H|E)". P(H|~E) tells you "OK, if E is impossible, my new probability for H is P(H|~E)". In the case of P(E) = 0.5, I will update by taking the mean of both.

Updating, proper updating, will only happen when you are certain of the probability of E (this is different form "being certain of E"), and the formulas will tell you by how much. Your joint probabilities are information themselves: they tell you how E relates to H. But you can't update on H until you know evidence about E.