Even though I have a dryer, I like to save energy.
They sell retractable clotheslines that you can use indoors. These are really very nice and convenient. The ones with 1 line are okay for light things (like underwear and socks) but they don't hold much and aren't for heavy things. But I bought one from Target.com that has 5 lines. It's a bit pricier than the others but it's very sturdy and holds a lot of clothes (if you hang them on the lines on hangers, you save even more space!). Definitely work the money for me. The best part is that you can put it anywhere because when you are not using it, the lines retract into the base (much, much better than having a line permanently across a room or having to constantly untie one!). I did a lot of shopping until I found the solution I liked. I recommend the 5-Line (especially since you have a large family and I'm sure a lot of clothes!).
8 ft. 1-Line: http://www.target.com/Whitney-Design-8-Retractable-Dryer/dp/B000JYEP1W/ref=sc_ri_5/601-1357890-5918525
40 ft. 1-Line: http://www.target.com/Whitney-Design-40-Retractable-Dryer/dp/B000JYFNY0/ref=sc_ri_6/601-1357890-5918525
34 ft. 5-Line: http://www.target.com/Whitney-Design-Retractable-5-Line-Dryer/dp/B000JY8V3U/ref=sc_ri_1/601-1357890-5918525
12 ft. Mini 5-Line: http://www.target.com/Whitney-Design-Retractable-5-Line-Dryer/dp/B000JYE2NI/ref=sc_ri_4/601-1357890-5918525
Another great and inexpensive method is to hang your clothes on hangers and use a tension shower curtain rod. You can use these in a space in your laundry room or anywhere in your house, even a hallway. You don't have to install anything, it doesn't damage your walls and it's easy to take down when your clothes are dry. It's just a skinny rod so it's easy to store (unlike those wood drying racks that take up a lot of space when and when not in use... they also don't hold much, collapse easily, and get moldy from the wet clothes).
If you don't have that much room or you aren't looking to spend anymore money, you can use places around your house to hang your clothes on hangers. The ledges on the tops of your door frames work well. If you hang the clothes on the doors of the rooms of their owners, they can easily put them away themselves when they're dry. The shower curtain rod in your bathtub also works well. I did this when we had an apartment. With these two methods, it was always best for me to do my laundry and let the clothes dry overnight so I could take them down in the morning and they wouldn't be in the way for the rest of the day.
Oh and having a dehumidifier in the room you hang your clothes in will get rid of excess moisture preventing mustiness, mold and it could help dry your clothes faster.
I hope this helps. Good luck!