There are four known and proven cases of a German Cross in Gold double award, that is it was awarded twice by the Heer and Luftwaffe (3), respectively the Heer and the Kriegsmarine (1) [de facto Doppelverleihung]. In three cases this occured for the same action, in one case this occured most probably for two different actions. It is not known if the awards and the documents were handed out twice in fact (recipient or relatives) and therefore the award has to be considered a double award officially [de jure]. Based on the general structure and practice of the awarding system it is to assume that these four cases happened by accident. Obviously specific circumstances made it possible that the parallel awarding channels of the Wehrmacht branches weren't combined for one single final approval and instead resulted in two awards.

Harazim, Georg-Wilhelm, Oberleutnant, Kp.Chef im Kampfbtl. Reggio / 15. Pz.Gren.Div.
[also called Pz.Gren.Btl. Reggio ; = ex Marsch-Btl. A 70 (or 69)]
11.12.1943 p.m. , Heer award
03.04.1944 p.m. , Luftwaffe award

Jäger, Walter, Martrosenobergefreiter d.R., Einzelkämpfer i. e. Frontaufklärungskommando im Westen, K.d.K.
06.10.1944 , Kriegsmarine award
03.10.1944 , [Obergefreiter] , Heer award
[remark : as a frogman Jäger participated in the blow up of the NIJMEGEN brigdes (railroad and car bridges over the River Waal) on 29 Sept 1944 (with To-Minen). A group of 12 men (3 teams of 4) destroyed one and damaged one bridge at least. 10 of them didn’t return (all went into captivity ; other sources : 3 were killed, 7 were captured). Jäger and Funkmaat Heinz Bretschneider who did belong to his group were the only ones who returned to their lines. Marine-Einsatz-Kommandos 60 and 65 were used for this operation and Jäger was assigned to one of those two Kommandos]

Schwarz, Heinrich, Hauptmann, II./Pz.Gren.Rgt. 2 "HG" / Fsch.Pz.Div. 1 "HG"
03.10.1944 , Heer award
01.01.1945 [date per announcement in Luftwaffen-Verordnungsblatt ("Ehrenliste der Luftwaffe" as addendum (Anlage)] , Luftwaffe award

Volkmer, Hans, Hauptmann
17.10.1943 , [Rgts.Adjutant] Pz.Gren.Rgt. 115 / 15. Pz.Gren.Div. [Luftwaffe award , Sicily]
05.09.1943 , Kdr. Marsch-Btl. A 30 / Division "von Manteuffel" [Heer award , North Africa, Tunisa]
[remark : Hptm Volkmer is the only recipient of the DKiG who was suggested and awarded twice for two different actions at two Theatres finally. For his service in Tunisia via the Heer and for his service on Sicily after the breakdown of HGr. Afrika via the Luftwaffe. This is the obvious conclusion based on the files available combined with the unit's histories he served with]

Sources used

Cajus Bekker - Einzelkämpfer auf See, 1978
Michael Jung - Sabotage unter Wasser: Die deutschen Kampfschwimmer im Zweiten Weltkrieg, Verlag E.S. Mittler & Sohn GmbH, Hamburg - Berlin - Bonn, 2004 , [ISBN 3-8132-0818-4]
Bernd Gericke - Die Inhaber des Deutschen Kreuzes in Gold, in Silber und die Inhaber der Ehrentafelspange der Kriegsmarine
Klaus Patzwall & Veit Scherzer - Das Deutsche Kreuz: Geschichte und Inhaber 1941-1945
Veit Scherzer - scherzers-militaer-nachrichten-de, article from March 2007