A mast assembly for a drilling rig includes a mast formed from a plurality of mast subunits. The mast assembly includes a lower drilling machine, upper drilling machine, and upper mud assembly, each of which is coupled to and movable vertically relative to the mast. The mast subunits are separable when the mast is in a transport configuration such that the LDM is positioned in a first subunit and the UDM is in a second subunit of the mast when the mast is in the transport configuration. The mast assembly may be used during a continuous drilling operation.