We have investigated the properties of two-mode squeezed states of various kinds: squeezed coherent states, squeezed number states, squeezed thermal states, and squeezed number-thermal states. The properties studied include characteristic functions, photon number distributions, and high-order moments. We show that a two-mode squeezed coherent state appears in either of its modes as a Glauber-Lachs superposition of a coherent signal with thermal noise; this generalizes the well-known thermofield result that a two-mode squeezed vacuum state behaves like a pure thermal state in either of its modes. We investigate the higher-order squeezing (in the sense of Hong and Mandel) of squeezed coherent-thermal and squeezed number-thermal states. Although the squeezing is found to increase with order in both cases, there are nevertheless interesting differences that can be traced to the fact that the Wigner function has a Gaussian form for the former but not for the latter.