idahochukar2,
The CMP maintains a list of past Distinguished Rifle and Pistol shots. I found your dad's name on the Pistol list, but not the Rifle list. He was also absent from the "Multiple" badge listing. Their list by their own admission is far from complete, and I'd bet they'd appreciate your updating them with the addition of your dad to the Rifle and "Multiple" listing.

Here's list to the CMP Distinguished listing;
http://clubs.odcmp.com/cgi-bin/report_distinguished.cgi

Other's have touched on this already, but I'll add my two cents worth. A few things such as the current service rifles and other gear have changed since your dad shot, but core elements remain and a Distinguished award of any flavor remains very highly thought of in Competitive shooting circles. To add some luster to your Dad's award...he achieved his awards when shooting was much larger than it is today. Matches were much larger and military support for competitive shooting was much greater back then...thus it was significantly more difficult to earn these awards. Jeff mentions badge numbers. I'd bet your dad's were awarded at a time before they started numbering civilian badges (there was no service affiliation noted on the CMP Pistol listing).
For more reading on the history and significance of your Dad's awards, read the linked articles;
http://www.odcmp.com/Competitions/Distinguished_History.pdf
http://www.odcmp.com/Competitions/In_Distinguished_Company_Culver_2000.pdf

Here are some pics of older medals from the 1920's and one from the 2000 time frame to compare.
[Linked Image]
[Linked Image]
Note the engraving style on the back along with the pins to attach the enameled "target" to the badge.

Here's the plated medals they're issuing these days;
[Linked Image]

Hopefully we can impart enough information about the significance of these medals that you'll be motivated to hang onto them as a piece of something your father enjoyed and achieved in. Better yet, may they inspire you to pursue the same challenges that he did.