The city-county library commission shall consist of eleven (11) members. Six of the members shall be appointed by the mayor of the city subject to approval of the governing body thereof. Three of the members shall be appointed by the board of county commissioners. The mayor of the city and the chairman of the board of county commissioners shall be ex officio members of the commission and shall be entitled to vote on all matters. The chairman of the board of county commissioners may designate another county commissioner to serve in place of the chairman on the commission. The county commissioner designated by the chairman shall have the same voting rights as the chairman of the board of county commissioners. The initial appointments by the city shall designate two members to serve a term of three (3) years, two members to serve a term of two (2) years, and two members to serve a term of one (1) year. The initial appointments by the county shall designate one member to serve a term of three (3) years, one member to serve a term of two (2) years, and one member to serve a term of one (1) year. Provided, that the terms of such initial appointees and the terms of all future appointees of both the city and county shall expire on July 31 of that year in which they expire, regardless of the calendar date when such appointments are made. Subsequent appointments of either the city or the county shall be for three-year terms, except in the case of an appointment to fill a vacancy in the membership of the commission, which latter appointment shall be for the balance of the unexpired term of the member whose death, resignation, or removal has created the vacancy. A member of such commission once qualified can thereafter be removed during his term of office only for misconduct or neglect of duty and, if he requests a hearing before the governing body by which he was appointed, after such hearing has been held. All members of the commission shall serve thereon without compensation. Expenses which are incurred by members pursuant to prior specific authorization by the board of county commissioners and the governing body of the city shall be reimbursed, provided that expenses incurred for transportation, meals, and lodging shall be reimbursed only if incurred in connection with authorized travel outside the county.