Especially early in the war, SS-units were often looked down upon by Wehrmacht officers. While everyone shared patriotism and nationalism, much of the officer corps of the Wehrmacht had roots in the nobility of old which was more attached to the old Kaiserreich that ceased to exist after WW1. The SS was a political formation based on Nazi ideology. This was especially true for the early units. The social backgrounds of those in command were often (but of course not always) cross. I'll try to make a somewhat awkward comparison: People who accept science and facts as a base of arguments don't go well together with those of a different 'ideology' which is based on 'alternate facts' (i.e. lies), negates science, etc. For the sake of the example, the SS would fit in the latter category. Wehrmacht units sometimes refused to give up some of their eqipment to forward it to early SS units, which were at that point often not as well equipped and had to use some captured equipment in some cases.
Later on, the SS expanded greatly. It ceased to be a volunteer force and people were drafted into it like into the Heer. The equipment of some of the early SS-Division was greatly improved - they were favored by the Nazi leadership for political reasons. They were preferred in receiving more and better weapons and reinforcements. These were the Divisions that won the renown for battle prowess (Das Reich and Totenkopf for example). Often, these Divisions or parts thereof acted as 'fire brigades' or spearheads in operations and thus Wehrmacht units were often glad if they had them as a neighbor and highly respected.
Late in the war, surprisingly, all sorts of non-Germans were used for SS-Divisions. I am not talking of Danish, Dutch or Skandinavians that the Nazis could consider 'aryan' and thus 'racially acceptable' but for example people from the Balkans etc. These late SS-Divisions were mostly mediocre at best.
As for the command structure:
Say, for example, a battered German Infantry Division received 'fire brigade' help by an SS-Regiment. This SS-Regiment would be despatched from its Division and subordinated to the command structure of the Wehrmacht Infantry Division. This is the way it worked on any level - from entire Divisons over Regiments, Battalions, Companies or even a single AFV Platoon. Regardless of what branches of German military was involved. So if you imagine a Wehrmacht Divison with an attached Fallschirmjäger Bataillon, to which a SS-Tank Platoon was in turn attached, then the SS-Tanks would be receiving orders from the Fallschirmjäger Bataillon, who in turn would be commanded by Wehrmacht Officers from the unit to which they were attached.
These attachements, subordinations etc. could change very quickly, especially late in the war. Think of various "Kampfgruppen" that were an assortment of units sometimes built on the spot in an improvised manner, sometimes created for a particular mission follwing a thorough plan.
This system worked quite well and was one of the strengths of the German military in WW2.
von Marwitz
