Double bar line suppresses following repeat bar line

[Patrick or Cynthia Karl]

The following snippet:

\version "2.18.0"

music = \relative b' {
   \repeat volta 2 { \repeat unfold 3 { c4 c c c } }
   \alternative {
        { c1 }
        { g1  }
   }
   
%   \bar "||"
   
   \break
   
   \repeat volta 2 { \repeat unfold 5 { a4 a a a } }
}

\score {
   \new Staff \music
   \layout {}
}

places a simple single bar line at the end of the 2nd alternative.  My client 
wishes it to be a double bar line instead.  I can do that by uncommenting the 
"\bar "||" line, but that has the unfortunate side effect of eliminating the 
initial repeat bar line of the following section.

Is there a way to place a double bar line at the end of the 1st line without 
interfering with the repeat bar line that follows?