Since you asked about "interpretation", let's interpret.
1. Literal definition of "picturesque"
Oxford Dictionaries: "(Of a place or building) visually attractive, especially in a quaint or charming way".
2. Her frame of mind
Disillusionment. She realises that "they blew him all to bits." This is vastly different from her earlier romanticised notion of war: "a wounded soldier appearing with a minor wound to re-join by coincidence his girlfriend." She previously had a fairy tale (or propaganda) notion of war.
3. What Hemingway wants to say
War blows everyone up into pieces, mentally, psychologically and physically.
4. Frederic's (the male character in this dialogue) frame of mind
Cynical. He teases her naivete: "This is the picturesque front." Of course no front in a war is in fact picturesque. He says this sarcastically.
5. Other things to note
a. The author paves the way for the development of the relationship between Frederic and Catherine (the girl speaking here) by telling us about their frame of mind.
b. When later on you read about Frederic being wounded, and Catherine nursing him, you will see this dialogue as a harbinger.
c. This dialogue is an indictment against war.
d. The contrast between "picturesque" and "blowing to bits" is an indictment against all who idealise war - politicians, movie producers, writers, journalists, ordinary people, everyone.
e. Read the First World War poets to understand more the journey from war euphoria to the utmost abhorrence, via profound disillusionment and horror.
f. First World War literature is a complete subject in itself in English Literature.
g. We are not only talking about WWI, but all wars.
h. The very word "picturesque" here, charged with irony, is supposed to carry, and evoke, the full weight of everything I wrote above in the mind of the informed and intelligent reader.
So that was a bit of an interpretation for you.