A connector assembly for interconnecting optical and/or electrical conductors comprises first (1) and second (2) connector parts. Each connector part is provided with an alignment piece (3, 10) with alignment channels (4) for first and second conductors, respectively. Each conductor (11) includes a contact pad in the upper surface of the corresponding alignment piece. The first alignment piece (3) is provided with a reference slot (18) with straight first reference faces (13, 20) and the second alignment piece (10) is provided with a reference projection (28) with straight second reference faces (29, 30) which abuts the first reference face in the coupled position of the connector parts. The reference faces are located at an accurately determined location with respect to the guiding channels. The alignment pieces (3, 10) comprise a support plate (15, 25) and a guiding plate (16, 26) manufactured with very high accuracy. At least the ends of the guiding channels are formed in the guiding plate. The reference slot and the reference projection, respectively, are part of the guiding plate.