The newly designed fonts in recent years for Chinese have much better Roman parts which are already distributed by operating system or could obtained for free:
- Microsoft YaHei in Windows http://www.fonts.com/font/microsoft-corporation#product_top
- Hiragino Sans GB in Mac (http://blog.jjgod.org/2009/06/04/updates-on-font-changes-in-...)
- Source Han Sans free from Adobe (http://blog.typekit.com/2014/07/15/introducing-source-han-sa...)
Many Chinese websites have already using one of them as their default font. There are also a dozen of commercial Chinese fonts which contain higher quality Roman typeface (although could not catch up most classic ones).
And for professionals (like book publishers or designers) in China, they often combine one Chinese font and one Roman font in their product for better result. (e.g. FZNew ShuSong + Sabon for Serif).