Surface microfluidics, offering unique flow characteristics and addressing intrinsic interfacial problems encountered in microfluidic systems, becomes an attractive alternative to the conventional closed-channel counterparts. Moreover, the planar structure in surface microfluidics enables simple microfabrication, while the open-surface platform allows direct fluidic operations and easy surface modification. In the paper, we first present novel three-dimensional microfluidic manipulations utilizing the unique flexible gas-liquid interface on surface microfluidic platform. The surface-micropatterned triple lines, defining the gas/liquid/solid interfacial boundaries, play an important role in determining the microflow profile. Specifically, the distinct elastic gas-liquid interface enables time-dependent (capacitive) and three-dimensional (deformable) operations of the flow, in contrast to the primary linear (resistive) nature of conventional microfluidics. Spatiotemporally dependent flow patterns on the planar microfluidic surfaces have been theoretically analyzed and experimentally controlled. Utilizing the distinct flow characteristics, new surface microfluidic functionalities, such as microflow regulation and flow rate-controlled switching, have been established. Furthermore, 3D surface microfluidic networks have been fabricated by fluidic connection of two independent planar surfaces, and microflow multiplexers with two-level flow-switching have been successfully devised to illustrate its potential in digital microfluidics.