We present the analysis of the first 18 months of data obtained with the COSMOSOMAS (COSMOlogical Structures On Medium Angular Scales) experiment at the Teide Observatory (Tenerife). Three maps have been obtained at 12.7, 14.7 and 16.3GHz covering 9000deg2 each with a resolution of ~1° and with sensitivities 49, 59 and 115μKbeam-1, respectively. These data in conjunction with the Wilkinson Microwave Anisotropy Probe (WMAP) first year maps have revealed that the cosmic microwave background (CMB) is the dominant astronomical signal at high galactic latitude (|b| > 40°) in the three COSMOSOMAS channels with an average amplitude of 29.7 +/- 1.0μK (68 per cent c.l. not including calibration errors). This value is in agreement with the predicted CMB signal in the COSMOSOMAS maps using the best-fitting Λ-CDM model to the WMAP power spectrum. Cross-correlation analysis of the 408-MHz map and the COSMOSOMAS data at high galactic latitudes give values in the range 17.0-14.4μK from 12.7 to 16.3GHz. Removing detected point sources in this template, reduces the amplitude of the correlated signal to 8-9μK. The mean spectral index of the correlated signal between the 408MHz desourced and the COSMOSOMAS maps is between -3.20 and -2.94 at |b| > 40° which indicates that this signal is due to synchrotron emission. Cross-correlation of COSMOSOMAS data with the Diffuse Infrared Background Experiment (DIRBE) map at 100μm shows the existence of a common signal with amplitude 7.4 +/- 1.1, 7.5 +/- 1.1 and 6.5 +/- 2.3μK in the 12.7, 14.7 and 16.3GHz COSMOSOMAS maps at |b| > 30°. Using the WMAP data, we find this DIRBE correlated signal rises from high to low frequencies flattening below ~20GHz. At higher galactic latitudes the average amplitude of the correlated signal with the DIRBE maps decreases slightly. The frequency behaviour of the COSMOSOMAS/WMAP correlated signal with DIRBE is not compatible with the expected tendency for thermal dust. A study of the Hα emission maps do not support free-free as a major contributor to that signal. Our results provide new evidence of a Galactic foreground with properties compatible with predictions by spinning dust models.