This paper presents the optical design of a miniature 3D scanning system, which is fully compatible with the vertical integration technology of micro-opto-electro-mechanical systems (MOEMS). The constraints related to this integration strategy are considered, resulting in a simple three-element micro-optical setup based on an afocal scanning microlens doublet and a focusing microlens, which is tolerant to axial position inaccuracy. The 3D scanning is achieved by axial and lateral displacement of microlenses of the scanning doublet, realized by micro-electro-mechanical systems microactuators (the transmission scanning approach). Optical scanning performance of the system is determined analytically by use of the extended ray transfer matrix method, leading to two different optical configurations, relying either on a ball lens or plano-convex microlenses. The presented system is aimed to be a core component of miniature MOEMS-based optical devices, which require a 3D optical scanning function, e.g., miniature imaging systems (confocal or optical coherence microscopes) or optical tweezers.