Subcycle strong-field ionization (SFI) underlies many emerging spectroscopic probes of atomic or molecular attosecond electronic dynamics. Extending methods such as attosecond high harmonic generation spectroscopy to complex polyatomic molecules requires an understanding of multielectronic excitations, already hinted at by theoretical modeling of experiments on atoms, diatomics, and triatomics. Here, we present a direct method which, independent of theory, experimentally probes the participation of multiple electronic continua in the SFI dynamics of polyatomic molecules. We use saturated (n-butane) and unsaturated (1,3-butadiene) linear hydrocarbons to show how subcycle SFI of polyatomics can be directly resolved into its distinct electronic-continuum channels by above-threshold ionization photoelectron spectroscopy. Our approach makes use of photoelectron-photofragment coincidences, suiting broad classes of polyatomic molecules.