"A humble child" is correct. The use of "a" or "an" is determined by sound, not spelling. The "h" in the word "humble" is pronounced as a consonant sound (as in hum), not a vowel sound, so "a" is correct. Similarly with "hundred", the "h" is pronounced as in "hun", so "a hundred miles" is correct.
Some words begin with a silent "h", meaning the word begins with a vowel sound, in which case "an" is correct:
(1) "It was anhonour to meet him".
(2) "It will take about anhour".
In (1) "honour" begins with a silent "h", so it is pronounced with a vowel sound at the beginning, rather like "on-er". The same applies in (2): the "h" is silent, so it is pronounced rather like "ow-er" with a vowel sound at the beginning.