We present new Spitzer/InfraRed Array Camera (IRAC) observations of 55 dusty long-period variables (48 asymptotic giant branch, AGB, and 6 red supergiant stars) in the Galaxy that have different chemistry, variability type, and mass-loss rate. O-rich AGB stars (including intrinsic S-type) tend to have redder [3.6]-[8.0] colours than carbon stars for a given [3.6]-[4.5] colour due to silicate features increasing the flux in the 8.0-?m IRAC band. For colours including the 5.8 ?m band, carbon stars separate into two distinct sequences, likely due to a variable photospheric C3 feature that is only visible in relatively unobscured, low mass-loss rate sources. Semiregular variables tend to have smaller infrared (IR) excess in [3.6]-[8.0] colour than Miras, consistent with the hypothesis that semiregular variables lose mass discontinuously. Miras have redder colours for longer periods while semiregular variables do not. Galactic AGB stars follow the period-luminosity sequences found for the Magellanic Clouds. Mira variables fall along the fundamental pulsation sequence, while semiregular variables are mostly on overtone sequences. We also derive a relationship between mass-loss rate and [3.6]-[8.0] colour. The fits are similar in shape to those found by other authors for AGBs in the Large Magellanic Cloud, but discrepant in overall normalization, likely due to different assumptions in the models used to derive mass-loss rates. We find that IR colours are not unique discriminators of chemical type, suggesting caution when using colour selection techniques to infer the chemical composition of AGB dust returned to the interstellar medium.
