People who back up their digital photos, videos and documents usually do so in one of two places—a giant hard drive in their home, or a giant remote storage facility in the cloud. If one of these storage solutions goes kaput, so can the data.

Isn’t there a better way?

For the past week, I have been testing Space Monkey, a storage solution that promises to save your data both locally and remotely. The best of both worlds doesn’t come cheap, at least not at first glance: For $199 you get a one-terabyte drive that looks like a large capsule, plugs into your wireless router and stores any files you copy to it. But what sets Space Monkey apart is its peer-to-peer backup system, ensuring that your files are also stored remotely on multiple devices. This service is free for the first year and $49 a year after that.

I like the way Space Monkey works, doubling up on backups and giving me fast access to my data. Saved files were easy to access remotely using login credentials. But its interface is a little sparse, and on the computer it’s missing a one-click feature that would automatically move all files over to Space Monkey.

Peer-to-peer backup technology can be tough to understand. In short, every Space Monkey drive comes with one terabyte of storage that you can use for storing your own files plus a second, hidden terabyte of storage that the company uses for storing bits of other people’s files. Any time anyone saves a file in Space Monkey, it’s encrypted, chopped into tiny pieces and stored in up to 40 different drives belonging to other users. This means that anyone trying to get to your files would need to access each of these devices and decrypt the files.

The idea of peer-to-peer networks has been tried before, including on CrashPlan, which I reviewed last year. But Space Monkey aims to use the technology in a way that doesn’t require geeky tinkering on your end, nor does it require a big chunk of your computer’s hard drive for shared storage.

It costs a lot less for a company to use this method compared with running a data-storage center, as competitors’ prices show. Dropbox, for example, charges $795 a year for its one-terabyte storage option. Space Monkey’s subscription is $49 a year.

Once your file is saved on Space Monkey, you can access it anywhere, including remotely from mobile devices or from other computers using the Space Monkey Web app. If you know you’ll be offline while trying to use one of your saved files, you can pin and save the file in a way that makes it locally accessible.

After you install the Space Monkey app on your phone, you log into your account and use the app as an automatic backup for all of your photos and videos. This is a big relief for me as a new mom, so I know my dozens of baby photos and videos are backed up in two ways.

But Space Monkey needs a better interface. While it prides itself on being simple, it also left me wondering if and when it was working. I had to ask the company’s founders how certain features functioned because I didn’t see obvious instructions in the device’s app or desktop interface.

Unlike the app, Space Monkey used on a computer doesn’t yet offer a way to automatically save all of someone’s files, or all of one type of file, such as photos. Currently, people have to drag and drop to move files or folders over to Space Monkey, or right-click each folder or file and select “Copy to Space Monkey.”

The thought of storing your data with an unfamiliar company may make you nervous, though Space Monkey’s founders have years of experience with data backup technology. And if worse comes to worse, you’ll still have your one-terabyte drive that will function as a destination for backed-up files.

After setting up Space Monkey in my house, I created an account using an email and password, then installed Space Monkey software on two computers. My husband wanted to store his files on our Space Monkey account, too, and though we currently have to share an account to do this, Space Monkey’s founders said that by the start of next year, multi-account features will work for families and small businesses.

If you use Time Machine, Apple’s built-in backup software, you can point it to your Space Monkey drive for storage, though this feature is still in its initial phase.

When I downloaded and installed the Space Monkey app on an iPhone and an Android phone, an option during setup asked if I wanted to back up photos over cellular. This is turned off by default so that people back up photos only when in Wi-Fi to avoid higher monthly data fees.

Space Monkey’s Android app includes all images from your phone’s Gallery, and this could mean that you’re backing up random images that other apps may have put in your Android Gallery. In my case, this included random images from Facebook that at some point I had come across in my Facebook News Feed and didn’t realize had been saved onto my phone. Space Monkey’s co-founder, Alen Peacock, said this is due to the way Android stores these images on your phone.

Though Space Monkey’s peer-to-peer storage solution can be intimidating and tough to understand, its double-safe backup provides peace of mind without monkeying around.

Write to Katie at katie.boehret@wsj.com