Should be more common place than imagined, the most famous example that I know of: English Premier League 2001-02 : Arsenal FC H/A: P W D L GF - GA Pts GD Overall: 38 26 9 3 79 - 36 87 (+43) Home: 19 12 4 3 42 - 25 40 (+17) Away: 19 14 5 0 37 - 11 47 (+26)
Another: Australian A-League 2012-13 : W. Sydney Wanderers FC H/A: P W D L GF - GA Pts GD Overall: 27 18 3 6 41 - 21 57 (+20) Home: 14 8 2 4 19 - 13 26 (+6) Away: 13 10 1 2 22 - 8 31 (+14)
One more: USA MLS 1998 : Los Angeles Galaxy FC H/A: P W D L GF - GA Pts GD Overall: 32 22 4 6 85 - 44 70 (+41) Home: 16 10 3 3 41 - 21 33 (+20) Away: 16 12 1 3 44 - 23 37 (+21)
(Spain) Most points in a season away: 50, Real Madrid (2011–12) however, this record breaks even with their home record of that season; 16wins 2draws 1loss
To clarify, in their unbeaten season (2003/04), Arsenal had a better home record vs away. Home: 1. Arsenal FC 19 15 4 0 40 - 14 49 (+26) Away: 1. Arsenal FC 19 11 8 0 33 - 12 41 (+21)