That sounds exactly like a weekly news magazine. There are quite a few that are worth reading, if you want to follow the news. The slower publishing pace allows a greater perspective and context on most stories that is missing on 24/7 channels.
Could you post some examples? Specifically ones that center on world news and not only the US / Europe.
The Economist. Albeit overtly liberal (in European sense), the content is well written, well discussed and subscription policy is great.
The Week [1] is an excellent subscription magazine that comes every Friday to my door. It's UK-centric, but has international news as one of its many sub-sections.