The target and double spin asymmetries of the exclusive pseudoscalar channel were measured for the first time in the deep-inelastic regime using a longitudinally polarized 5.9 GeV electron beam and a longitudinally polarized proton target at Jefferson Lab with the CEBAF Large Acceptance Spectrometer (CLAS). The data were collected over a large kinematic phase space and divided into 110 four-dimensional bins of , , −t and ϕ. Large values of asymmetry moments clearly indicate a substantial contribution to the polarized structure functions from transverse virtual photon amplitudes. The interpretation of experimental data in terms of generalized parton distributions (GPDs) provides the first insight on the chiral-odd GPDs and , and complement previous measurements of unpolarized structure functions sensitive to the GPDs and . These data provide a crucial input for parametrizations of essentially unknown chiral-odd GPDs and will strongly influence existing theoretical calculations based on the handbag formalism.