Studies of edge-on spiral galaxies have revealed a number of cases in which kiloparsec-scale H I features extend from the disk into the halo region. We have obtained VLA CnB array 21 cm H I observations of NGC 2613, an edge-on spiral galaxy 26 Mpc away. We report that NGC 2613 is an extremely massive galaxy with a nearby companion galaxy (ESO 495-G017). We present the first H I maps and masses for this companion. We have found three high-latitude features above the plane, symmetric in projection with three below the plane in NGC 2613. All six features show a multiple velocity structure, with several ``spurs,'' as well as a trend to lag behind the disk gas with increasing distance from the plane. The radio continuum emission shows two large extensions associated with a strong continuum source in the disk. These are the highest latitude discrete features clearly connected to a spiral galaxy yet detected in radio continuum. Moreover, two of the H I features show a strong correlation with these large continuum extensions, with the continuum arranged on the perimeter of the H I. We postulate that these features were formed by some mechanism internal to the galaxy, possibly by spatially correlated supernovae or by the action of a preexisting relativistic jet flowing through the plane of the galaxy.