A splice connects a lower coiled tubing segment containing a lower power cable segment to an upper coiled tubing segment containing an upper power cable segment. The splice has a lower terminal electrically connecting together upper ends of lower power conductors. An upper terminal electrically connects together lower ends of upper power conductors. An electrical intermediate connector has an upper end that stabs into engagement with the upper electrical terminal and a lower end that stabs into engagement with the lower electrical terminal. A load supporting member surrounds the intermediate connector and joins to upper and lower ends, respectively, of the lower coiled tubing segment and the upper coiled tubing segment.