This should work for you:
sed -n '/\*\//q; /^\/\*/d; s/^ \* \?//p' <file.h >comment.txt
Here's the explanation: sed (as you know) is a command that goes through a file, applying a list of rules to each line. Each rule consists of a “selector” and commands that apply to this line only if the selector matches.
/\*\//. ; , */. , . ( , .) q, "". sed . , -n, " , ".
/^\/\*/, , /* . , , . d sed .
, ( ). s/PATTERN/REPLACEMENT/, , . ^ \* \?, , 0 1 , . . , sed - ()? . p , sed . - -n.