Resonance enhanced two photon ionization study in a pulsed molecular beam identified spin-forbidden transitions of the 2 (3)Pi(u)(1(u))-X (1)Sigma(g)(+)(0(g)(+)) and 2 (3)Pi(u)(0(u)(+))-X (1)Sigma(g)(+)(0(g)(+)) of Rb-2. Lambda-doubling and interference-induced rotational branch intensity anomalies are observed for 2 (3)Pi(u)(1(u))-X (1)Sigma(g)(+)(0(g)(+)) transitions. The rotational constant for the 2 (3)Pi(u) state was determined to be B-e=0.018 932 5 +/- 0.000 007 4 cm(-1) for Rb-85(2), giving R-e=4.5796 +/-0.0009 Angstrom. Other molecular parameters for Rb-85(2) are determined as T-e=19 784.254 +/- 0.009 cm(-1), omega(e)=42.200 +/- 0.006 cm(-1), omega(e)x(e)=0.171 +/- 0.001 cm(-1), and omega(e)y(e)=-0.001 06 +/- 0.000 06 cm(-1) for the 2 (3)Pi(u)(0(u)(+)) state and T-e=19 785.74 +/- 0.01 cm(-1), omega(e)=42.297 +/- 0.005 cm(-1), omega(e)x(e)=0.1725 +/-0.0009 cm(-1), and omega(e)y(e)=-0.000 78 +/- 0.000 04 cm(-1) for 2 (3)Pi(u)(1(u)) state. These R-e, omega(e), and T-e values agree well with ab initio calculated values. The spin-orbit coupling constant A and Lambda-doubling parameters p and q are determined by simultaneous fitting of the rotational structures of both 2 (3)Pi(u)(1(u))-X (1)Sigma(g)(+) and 2 (3)Pi(u)(0(u)(+))-X (1)Sigma(g)(+) transitions.