@gloriamer , from what you have posted, my understanding :
(a) You a US person ( citizen/GreenCard / Resident for Tax purposes ) being taxed by the US on world income;
(b) I don't know whether your tax home is US or not but certainly Germany is not -- that is because you are talking only about Dividend income being taxed at source. Thus there is no recovery ( i.e. no way to get Germany to " Not Tax" German sourced income.
(c) US-German Tax Treaty does not provide any direct benefit. However , because of the Double Taxation clause, you would be able to get substantial mitigation of the double bite / taxation on the same income.
(d) Note that when you file US return and you declare your German sourced dividend income and the taxes thereon ( by German Taxing Authority ), you may be able to use the "Safe Harbor" ---- US$300 foreign tax on passive income per filer --- to get full refund of the tax ( this is non-refundable i.e. it can only reduce your US tax burden but not below zero ).
Does this make sense ? Is there more can do for you ?