Mode-I fracture exhibits microbranching in the high velocity regime where the simple straight crack is unstable. For velocities below the instability, classic modeling using linear elasticity is valid. However, showing the existence of the instability and calculating the dynamics post-instability within the linear elastic framework is difficult and controversial. The experimental results give several indications that the microbranching phenomena is basically a three-dimensional phenomena. Nevertheless, the theoretical effort has been focused mostly in two-dimensional modeling. There some success has been achieved concerning the origin of the instability and the post-instability behavior, particularly within the context of atomistic simulations. In this work we study the microbranching instability using three-dimensional atomistic simulations, exploring the difference between the 2D and 3D models. We find that the basic 3D fracture pattern shares similar behavior with the 2D case. Nevertheless, some pure 3D experimental effects are reproduced by our simulations, and the quantitative features of the microbranches, separating the regimes of steady-state cracks (mirror) and post-instability (mist-hackle) are reproduced as well. We see a 3D-2D transition as the crack velocity increases, consistent with the experimental findings.