I had to do a good deal of research to be able to answer your questions and learned a number of things myself that, with my general knowledge of the time period, I think provides a good deal of insight.

First, lets establish a few broad things before we dive into details.

• Both the Blitz and the Allied bombing campaign against Germany targeted not only military installations but civilian cities as well; both the Axis and Allies used similar tactics. Both the Blitz and the Allied bombing campaigns were conducted in a mindset of 'total war'.

• In total war, the entirety of a nation's resources and population are part of the war machine supporting a campaign. Thus, the rationale for targeting civilians is quite simply that the definition of civilian is different. During a total war campaign, a civilian is a person who does not actively partake in front line combat, but supports the war effort through their labor and obedience.

• The Blitz was certainly designed to break the spirit of the British and lower their morale to a point where a land invasion of the United Kingdom would not be necessary, in addition to the pragmatic victories of limiting the ability to produce war material and keep the domestic population supplied. The Allied bombing campaign had similar if not identical goals.

I'm curious as to how the other side viewed this, if a common interpretation emerged during the bombings and if this continues to the present day?

The entire Second World War period is collectively remembered by the modern German people with a great deal of collective shame and distancing, and so trying to address how modern Germans understand their ancestor's "spirit" during this time is neither meaningful nor useful, I think. Rather, I'll be focusing primarily on the generation itself that experienced these events without trying to extrapolate to the present day.

Now with those broad things established, lets address your specific questions and compare and contrast how the Allied campaign was similar to and slightly different from the Blitz.

The Blitz "only" lasted from 7 September, 1940 – 11 May, 1941 while the Allies carried out its bombing campaign from 28 Mar 1942 - 3 Apr 1945. During the Blitz, about 60,000 civilians and 160,000 airmen were killed. The Battle of Britain occured from 10 July, 1940 – 31 October, 1940. More than a few conclusions can be drawn from these facts and figures alone: the German campaign to dominate airspace was a decisive failure. Allied air control over Britain and the English Channel boosted Allied morale and weakened German resolve. If the Battle of Britain had not been won by the Allies, the strategic bombing campaign of the Third Reich would have never taken place and we would not be having this discussion (or perhaps would be, but in German). German figures are much harder to come by due to the sheer mass destruction of the Allied campaign as well as Nazi sabotage of their own records in the very late war period; but anywhere from 353,000–635,000 German civilians were killed.

It's worth noting that the British sheltered the common Brit from bombings during the Blitz. In Germany, underground shelters and bunkers were reserved for the elite, command officers, and the most fit in keeping with the general attitude of the Reich at the time. As the Allied bombing campaign dragged on for years, many German citizens certainly felt betrayed by the Reich and this would later go on to help the process of Denazification.

The propaganda efforts during the bombing campaigns on either side were somewhat different. Generally, the Reich propaganda called for continued sacrifice and a willingness to die for the State while the British of course issued their now-famous "keep calm and carry on" campaign and by and large that was the general attitude of the British people; that is, they were able to trust their government and war effort to actually keep them safe enough to go about a normal life. By contrast, the life of the average German during the Allied campaign became a living hell. The United States Strategic Bombing Survey collected as much information as possible on how bombing affected both the Allies and their Axis enemies and found that sustained bombing did not serve to stiffen enemy morale, as some believed. Rather, it had the intended effect of deeply discrediting the Reich as the average German grew more and more tired of war. The Blitz by contrast did in fact serve to stiffen British resolve for two reasons: they had the certainty of continued material support from the United States and so whatever effect the German campaign had on their ability to produce war material was minute. Because the Third Reich was entirely self-reliant and even supported Italy with war material, whatever destruction the Allied campaign could wreak on the Reich was devestatingly effective.

I'll leave you with some of the words of German formal historians and amateur diarists and I hope their own words sufficiently explain just how different the German experience of bombing was from the British.

The poor people who stood at corners and in the squares with their few retrieved belongings but did not know where to go were a pitiful sight to behold. The authorities responsible for providing accommodation, such as the Red Cross, the security service, and deployed battalions, were all working at it at full speed, and consequently all homeless people could be accommodated in the evening, even if some of the solutions were only provisional. -- Dr. Franz Weimers, 9 July 1941 in Münster, Germany

[i]t's impossible! That many bombs cannot be dropped in a single night!" -- Luftwaffe commander Hermann Göring commenting on the Bombing of Köln, 30-31 May 1942

[W]e came upon places through which it was impossible to pass by car. Craters filled with water, heaps of rubble, firehoses, ... and convoys of lorries blocked the streets, where thousands of those rendered homeless were searching the ruins, trying to rescue some of their possessions, or were squatting on the pavements and being fed from field kitchens. -- 1 March 1943 Bombing of Berlin, Diary of Press officer Hans-Georg von Studnitz

We did not recognize our street anymore. Fire, only fire wherever we looked. Our 4th floor did not exist anymore. The broken remains of our house were burning. On the streets there were burning vehicles and carts with refugees, people, horses, all of them screaming and shouting in fear of death. I saw hurt women, children, old people searching a way through ruins and flames.... (A)ll the time the hot wind of the firestorm threw people back into the burning houses they were trying to escape from. I cannot forget these terrible details. I can never forget them. -- Lothar Metzger, nine year old civilian girl during the 13-14 Feb 1945 bombing of Dresden.

If you or anyone else have any follow up questions I'll be happy to look into those as well.

Bibliography

University of Exeter Centre for the Study of War, State and Society. https://humanities.exeter.ac.uk/history/research/centres/warstateandsociety/projects/bombing/germany/

C. Peter Chen. Bombing of Hamburg, Dresden, and Other Cities 28 Mar 1942 - 3 Apr 1945. https://ww2db.com/battle_spec.php?battle_id=55

Republic of Austria, The Unloved Democracy of the Inter-War Period. . https://web.archive.org/web/20060420214655/http://www.austria.org/history_rep.shtml

Kirwin, Gerald. Allied Bombing and Nazi Domestic Propaganda. First Published July 1, 1985 Research Article. https://doi.org/10.1177/026569148501500304

Rigole, Julius, "The strategic bombing campaign against Germany during World War II" (2002). LSU Master's Theses. 3268. https://digitalcommons.lsu.edu/gradschool_theses/3268

Kunt, Gergely. "A Female Adolescent Bystander's Diary and the Jewish Hungarian Holocaust." CLCWeb: Comparative Literature and Culture 17.3 (2015): https://doi.org/10.7771/1481-4374.2647

White, Matthew. Twentieth Century Atlas – Death Tolls: United Kingdom

Levine, Alan J. (1992). The Strategic Bombing of Germany, 1940–1945. Greenwood. ISBN 978-0-275-94319-6.

Collier, Basil. The Defence of the United Kingdom. HMSO, 1957.

The Strategic Bombing of Germany in World War II: Costs and Accomplishments Kenneth P. Werrell. The Journal of American History Vol. 73, No. 3 (Dec., 1986), pp. 702-713