We present measurements of the auto- and cross-frequency correlation power spectra of the cosmic (sub)millimeter background at 250, 350, and 500 μm (1200, 860, and 600GHz) from observations made with the Balloon-borne Large Aperture Submillimeter Telescope (BLAST); and at 1380 and 2030 μm (218 and 148GHz) from observations made with the Atacama Cosmology Telescope (ACT). The overlapping observations cover 8.6 deg2 in an area relatively free of Galactic dust near the south ecliptic pole. The ACT bands are sensitive to radiation from the cosmic microwave background, to the Sunyaev-Zel'dovich effect from galaxy clusters, and to emission by radio and dusty star-forming galaxies (DSFGs), while the dominant contribution to the BLAST bands is from DSFGs. We confirm and extend the BLAST analysis of clustering with an independent pipeline and also detect correlations between the ACT and BLAST maps at over 25σ significance, which we interpret as a detection of the DSFGs in the ACT maps. In addition to a Poisson component in the cross-frequency power spectra, we detect a clustered signal at 4σ, and using a model for the DSFG evolution and number counts, we successfully fit all of our spectra with a linear clustering model and a bias that depends only on redshift and not on scale. Finally, the data are compared to, and generally agree with, phenomenological models for the DSFG population. This study demonstrates the constraining power of the cross-frequency correlation technique to constrain models for the DSFGs. Similar analyses with more data will impose tight constraints on future models.