Grammar: Silent "h"
As in some dialects of English today, the "h" sound in Latin was not always pronounced. This means it is very easy for the "h" to fall out when someone is writing a word the way that it sounds. It also means that it is easy for an "h" to be put where it doesn't belong (an example of hypercorrection).
In later medieval Latin, you will regularly see the word mihi spelled michi. This does not mean that the "h" was being pronounced like the English sound "ch", and it does not mean that it was being strongly aspirated (like "kh"). It just means that the medieval Latin writers wanted to make it clear that this "h" was really and truly supposed to be pronounced, so that mihi would remain a two-syllable word. In order to make it clear that this was a sound that was supposed to be pronounced, they replaced the silent "h" with "ch".