Visible light communications (VLC) have emerged as a strong candidate for meeting the escalating demand for high data rates. In this paper, we consider a VLC network, where multiple access points (APs) serve both energy-harvesting users (EHUs), i.e., users who harvest energy from light emitted by diodes and information users (IUs), i.e., users who gather data information. In order to jointly balance the achievable sum rate at the IUs and the energy harvested by the EHUs, the paper considers maximizing a network-wide utility, which consists of a weighted sum of the IUs sum rate and the EHUs harvested energy, subject to individual IU rate constraint, individual EHU harvested-energy constraint, and AP power constraints, so as to jointly determine the direct current (DC) bias value at each AP, and the power of the alternating-current (AC) signals of the users. A difficult non-convex optimization problem is solved using an iterative approach which relies on inner convex approximations, and compensates for the used approximations using proper outer-loop updates. The paper further considers solving the special cases of the problem, i.e., maximizing the sum rate, and maximizing the total harvested-energy, both subject to the same constraints. Numerical results highlight the significant performance improvement of the proposed algorithms, and illustrate the impacts of the network parameters on the performance trade-off between the sum rate and harvested-energy.