Exploring new parameter regimes to realize and control novel phases of matter has been a main theme in modern condensed matter physics research. The recent discovery of two-dimensional (2D) magnetism in nearly freestanding monolayer atomic crystals has already led to observations of a number of novel magnetic phenomena absent in bulk counterparts. Such intricate interplays between magnetism and crystalline structures provide ample opportunities for exploring quantum phase transitions in this new 2D parameter regime. Here, using magnetic field- and temperature-dependent circularly polarized Raman spectroscopy of phonons and magnons, we map out the phase diagram of chromium triiodide (CrI3) that has been known to be a layered antiferromagnet (AFM) in its 2D films and a ferromagnet (FM) in its three-dimensional (3D) bulk. However, we reveal a novel mixed state of layered AFM and FM in 3D CrI3 bulk crystals where the layered AFM survives in the surface layers, and the FM appears in deeper bulk layers. We then show that the surface-layered AFM transits into the FM at a critical magnetic field of 2 T, similar to what was found in the few-layer case. Interestingly, concurrent with this magnetic phase transition, we discover a first-order structural phase transition that alters the crystallographic point group from C3i (rhombohedral) to C2h (monoclinic). Our result not only unveils the complex single-magnon behavior in 3D CrI3, but it also settles the puzzle of how CrI3 transits from a bulk FM to a thin-layered AFM semiconductor, despite recent efforts in understanding the origin of layered AFM in CrI3 thin layers, and reveals the intimate relationship between the layered AFM-to-FM and the crystalline rhombohedral-to-monoclinic phase transitions. These findings further open opportunities for future 2D magnet-based magnetomechanical devices.