You are right, Turnoi, hte "h" is not pronounced as per dictionary.com = /ˈɒnɪst/

Source: http://dictionary.reference.com/browse/honest :

Dictionary.com Unabridged (v 1.1) - Cite This Source - Share This
honest /ˈɒnɪst/ Pronunciation Key - Show Spelled Pronunciation
adjective
1. honorable in principles, intentions, and actions; upright and fair: an honest person.
2. showing uprightness and fairness: honest dealings.
3. gained or obtained fairly: honest wealth.
4. sincere; frank: an honest face.
5. genuine or unadulterated: honest commodities.
6. respectable; having a good reputation: an honest name.
7. truthful or creditable: honest weights.
8. humble, plain, or unadorned.
9. Archaic. chaste; virtuous.
[Origin: 12501300; ME honeste < MF < L honestus honorable, equiv. to hones- (var. s. of honōs) honor + -tus adj. suffix]

Related forms
honestness, noun

Synonyms 1. just, incorruptible, trusty, trustworthy. 2. fair. 4. straightforward, candid. 5, 9. pure.
Antonyms 1. dishonest, corrupt.