If we use good old calquing, we'll have встроенное размещение содержимого and размещение содержимого во вложении for "inline content disposition" and "attachment content disposition", respectively
This concept has apparently been taken from the email standards and originally said whether you should show a picture or a rich text snippet as a whole in the email body window or just as a filename in the attachments bar with a paper clip next to it.
This does not translate for browsers very well, even in English: a downloadable file is hardly an "attachment", or a PDF which opens in a new tab is hardly "inline"; and there is no envelope for the content to have "disposition" in it.
Those are just historical header names and values which had been reused for something completely different.
So my take on this would be just leaving the English terms as is:
При передаче данных сервер указывает способ обработки содержимого: "инлайн", если его нужно открыть в браузере, или "аттачмент", если его нужно сохранить в файл на диске.
or giving them a meaningful description, disregarding their English meanings:
При передаче данных сервер сообщает, являются ли они отображаемыми или сохраняемыми путём установки значения заголовка Content-Disposition
в inline
или attachment
, соответственно.
Again, you can't translate without a context, so if you want a useful answer, it would have been best if you provided a Russian phrase you are trying to build.