Sed Range of Patterns only if it contains Pattern

What i would like to know is how to print a Range of Patterns but only if it contains a specific Pattern.

For example:

I have a file that contains:

HEADER 1
AAA
BBBBBBB
MSG:testing
CCCCCC
DDD
PAGE 1

HEADER 2
EEE
FFFFFF
GGG
HHH
PAGE 2

I want to print from any HEADER to any PAGE but only if it contains the pattern MSG

The result i want is to print only these section:

HEADER 1
AAA
BBBBBBB
MSG:testing
CCCCCC
DDD
PAGE 1

What i have so far is: sed -n -e '/HEADER /,/PAGE /p' inputfile.txt > outputfile.txt

I'm open to any suggestions including the usage of Awk or Grep.

Thanks in advance.