Ultrasound-driven oscillating microbubbles are used as active actuators in microfluidic devices to perform manifold tasks such as mixing, sorting, and manipulation of microparticles. A common configuration consists of side bubbles created by trapping air pockets in blind channels perpendicular to the main channel direction. This configuration consists of acoustically excited bubbles with a semicylindrical shape that generate significant streaming flow. Because of the geometry of the channels, such flows are generally considered as quasi-two-dimensional. Similar assumptions are often made in many other microfluidic systems based on flat microchannels. However, in this Letter we show that microparticle trajectories actually present a much richer behavior, with particularly strong out-of-plane dynamics in regions close to the microbubble interface. Using astigmatism particle-tracking velocimetry, we reveal that the apparent planar streamlines are actually projections of a stream surface with a pseudotoroidal shape. We, therefore, show that acoustic streaming cannot generally be assumed as a two-dimensional phenomenon in confined systems. The results have crucial consequences for most of the applications involving acoustic streaming such as particle trapping, sorting, and mixing.