You want to associate a video file to be opened with Media Player Classic - Home Cinema. So, you right-click on the video file, choose Open With → Choose default program and MPC-HC is not listed there. So, you click Browse, find the location of the MPC-HC executable and choose it. But, MPC-HC still does not appear in the Open With dialog!
This is a weird behavior of MPC-HC. One way to solve this is to open MPC-HC and choose View → Options. Choose Player → Formats. In the Association section click on Modify, you will need to provide Administrator privileges for this. In the File Extensions list, choose all the video file extensions which you want to be associated with MPC-HC and click OK.
This setting takes effect immediately and when you right-click on a video file and choose Open With, MPC-HC should already be listed there now.
Tried with: Media Player Classic - Home Cinema (64-bit) 18.104.22.16802 and Windows 7 64-bit