A Doppler-free absorption spectrum and the Zeeman effect of the A B-1(2u)(v(14)=1,v(1)=1)<--X (1)A(1g)(v=0) transition of benzene have been measured by means of two-photon absorption spectroscopy with counterpropagating light beams of identical wavelength within an external cavity. Rotational lines were fully resolved, and 647 Q(Q) lines of J=0-43, K=0-43 have been assigned. The molecular constants of the A B-1(2u)(v(14)=1,v(1)=1) state have been determined as A=B=0.181 046 1, C=0.090 548 9, D-J=0.544x10(-7), D-JK=-1.093x10(-7), D-K=0.587x10(-7), and T-0=40 578.2672 cm(-1). The Zeeman splittings for lines of a given J were observed to increase regularly with K and reach a maximum at K=J. This demonstrates that the magnetic moment lies along the c axis (perpendicular to the molecular plane). The magnetic moment of the A B-1(2u)(v(14)=1,v(1)=1,J=43,K=43) level was determined to be 0.005 mu (B). The Zeeman splittings of the K=J levels were observed to increase with increasing J. Via analysis of the rotationally resolved Zeeman spectra, it is concluded that the A B-1(2u) state is mixed with the E-3(2u) state. This new finding suggests that vibronic interactions between E-3(2u) and B-3(1u)(T-1) and between E-3(2u) and E-3(1u)(T-2) through the mixed E-3(2u) component, contribute to the B-1(2u)(S-1)--> B-3(1u)(T-1) and B-1(2u)(S-1)--> E-3(1u)(T-2) intersystem crossings, respectively.